JEE Mathematics Matrices MCQs Set 17

Multiple Choice Questions (MCQs) for JEE Mathematics: Matrices

Access targeted multiple-choice questions for Matrices designed to align with the latest JEE academic syllabus for JEE Mathematics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Practice Matrices MCQs for JEE Mathematics

Navigate directly to the 50 objective questions for Matrices using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: The matrix \( A=\begin{bmatrix}-5&-8&0\\3&5&0\\1&2&-1\end{bmatrix} \) is
(a) idempotent matrix
(b) involutory matrix
(c) nilpotent matrix
(d) None of these
Show Answer & Explanation

Answer: (b) involutory matrix

Explanation:
1. Compute A²: the first row is (25 − 24, 40 − 40, 0) = (1, 0, 0), the second row is (−15 + 15, −24 + 25, 0) = (0, 1, 0), and the third row is (−5 + 6 − 1, −8 + 10 − 2, 1) = (0, 0, 1).
2. So A² = I, which means A is involutory.

Teacher's Note:
1. Square the matrix and compare with I.

Question 2: If Ak = 0 (A is nilpotent with index k), then (I − A)p = I + A + A² + ... + Ak−1 for p equal to
(a) −1
(b) −2
(c) \( \frac12 \)
(d) None of these
Show Answer & Explanation

Answer: (a) −1

Explanation:
1. (I − A)(I + A + ... + Ak−1) = I − Ak = I.
2. So I + A + ... + Ak−1 = (I − A)−1, and p = −1.

Teacher's Note:
1. Multiply the sum by (I − A).

Question 3: The matrix \( A=\begin{bmatrix}1&3&2\\1&x-1&1\\2&7&x-3\end{bmatrix} \) will have an inverse for every real number x except for
(a) \( x=\frac{11\pm\sqrt5}{2} \)
(b) \( x=\frac{9\pm\sqrt5}{2} \)
(c) \( x=\frac{11\pm\sqrt3}{2} \)
(d) \( x=\frac{9\pm\sqrt3}{2} \)
Show Answer & Explanation

Answer: (a) \( x=\frac{11\pm\sqrt5}{2} \)

Explanation:
1. A has an inverse unless det A = 0.
2. Expanding along the first row: det A = 1[(x − 1)(x − 3) − 7] − 3[(x − 3) − 2] + 2[7 − 2(x − 1)] = x² − 11x + 29.
3. x² − 11x + 29 = 0 has discriminant 121 − 116 = 5.
4. So x = (11 ± √5)/2.

Teacher's Note:
1. Set the determinant equal to zero.

Question 4: If A and B are two matrices such that AB = A and BA = B, then which one of the following is correct?
(a) \( (A^T)^2=A^T \)
(b) \( (A^T)^2=B^T \)
(c) \( (A^T)^2=(A^{-1})^{-1} \)
(d) None of the above
Show Answer & Explanation

Answer: (a) \( (A^T)^2=A^T \)

Explanation:
1. A² = A(A) = (AB)A = A(BA) = AB = A, so A is idempotent.
2. Then (AT)² = (A²)T = AT.

Teacher's Note:
1. Show first that A² = A.

Question 5: If \( A=\begin{bmatrix}1&0&0\\0&1&0\\a&b&-1\end{bmatrix} \) and I is the unit matrix of order 3, then A² + 2A⁴ + 4A⁶ is equal to
(a) 7A8
(b) 7A7
(c) 8I
(d) 6I
Show Answer & Explanation

Answer: (a) 7A8

Explanation:
1. A² = I (the third row gives (a − a, b − b, 1)), so A⁴ = A⁶ = A⁸ = I.
2. A² + 2A⁴ + 4A⁶ = 7I = 7A⁸.

Teacher's Note:
1. Compute A² first.

Question 6: Let \( A=\begin{bmatrix}1&2\\3&4\end{bmatrix} \) and \( B=\begin{bmatrix}a&0\\0&b\end{bmatrix} \), where a, b are natural numbers. Then which one of the following is correct?
(a) There exist more than one but finite number of B's such that AB = BA
(b) There exists exactly one B such that AB = BA
(c) There exist infinitely many B's such that AB = BA
(d) There cannot exist any B such that AB = BA
Show Answer & Explanation

Answer: (c) There exist infinitely many B's such that AB = BA

Explanation:
1. AB = [[a, 2b], [3a, 4b]] and BA = [[a, 2a], [3b, 4b]].
2. AB = BA needs 2b = 2a and 3a = 3b, i.e. a = b.
3. Every natural number a = b works, so there are infinitely many such B.

Teacher's Note:
1. Equate the entries of AB and BA.

Question 7: Elements of a matrix A of order 10 × 10 are defined as aij = ωi+j (where ω is a cube root of unity). Then tr(A) of the matrix is
(a) 0
(b) 1
(c) 3
(d) None of these
Show Answer & Explanation

Answer: (d) None of these

Explanation:
1. tr(A) = Σ ω2i for i = 1, ..., 10.
2. The powers ω², ω⁴, ω⁶ repeat with period 3 and sum to 0 over each block; the first nine terms sum to 0.
3. The tenth term is ω²⁰ = ω², which is none of 0, 1, 3.

Teacher's Note:
1. Group the terms in blocks of three.

Question 8: If B, C are square matrices of order n and if A = B + C, BC = CB, C² = O, then for any positive integer N, AN+1 = BK[B + (N + 1)C]. Then K/N is
(a) 1
(b) \( \frac12 \)
(c) 2
(d) None of these
Show Answer & Explanation

Answer: (a) 1

Explanation:
1. Since B and C commute, the binomial theorem applies: (B + C)N+1 = BN+1 + (N + 1)BNC + terms with C² = O.
2. This equals BN[B + (N + 1)C], so K = N and K/N = 1.

Teacher's Note:
1. Use the binomial theorem for commuting matrices.

Question 9: If \( A=\begin{bmatrix}0&-1\\1&0\end{bmatrix} \), then A¹⁶ is equal to
(a) \( \begin{bmatrix}0&-1\\1&0\end{bmatrix} \)
(b) \( \begin{bmatrix}0&1\\1&0\end{bmatrix} \)
(c) \( \begin{bmatrix}-1&0\\0&1\end{bmatrix} \)
(d) \( \begin{bmatrix}1&0\\0&1\end{bmatrix} \)
Show Answer & Explanation

Answer: (d) \( \begin{bmatrix}1&0\\0&1\end{bmatrix} \)

Explanation:
1. A² = −I, so A⁴ = I.
2. A¹⁶ = (A⁴)⁴ = I.

Teacher's Note:
1. Find the smallest power of A that equals I.

Question 10: Let \( A=\begin{bmatrix}x+y&y\\2x&x-y\end{bmatrix}, B=\begin{bmatrix}2\\-1\end{bmatrix} \) and \( C=\begin{bmatrix}3\\2\end{bmatrix} \). If AB = C, then A² is equal to
(a) \( \begin{bmatrix}6&-10\\4&26\end{bmatrix} \)
(b) \( \begin{bmatrix}-10&5\\4&24\end{bmatrix} \)
(c) \( \begin{bmatrix}-5&-6\\-4&-20\end{bmatrix} \)
(d) \( \begin{bmatrix}-5&-7\\-5&20\end{bmatrix} \)
Show Answer & Explanation

Answer: (a) \( \begin{bmatrix}6&-10\\4&26\end{bmatrix} \)

Explanation:
1. AB = C gives 2(x + y) − y = 3, i.e. 2x + y = 3, and 4x − (x − y) = 2, i.e. 3x + y = 2.
2. Subtracting: x = −1 and y = 5, so A = [[4, 5], [−2, −6]].
3. A² = [[16 − 10, 20 − 30], [−8 + 12, −10 + 36]] = [[6, −10], [4, 26]].

Teacher's Note:
1. Find x and y from the equation AB = C.

Free study material for Matrices

Multiple Choice Questions (MCQs) for JEE Mathematics Matrices

Download Multiple Choice Questions: Matrices (JEE Mathematics)

Review structured objective questions for JEE Mathematics Matrices. Built according to official JEE guidelines, these MCQ sets support daily revision and core concept reinforcement.

Concept Clarification for Matrices

Cross-reference your completed choices with comprehensive NCERT solutions for JEE Mathematics to ensure absolute clarity across all sub-topics in this chapter.

Additional Study Resources for JEE Mathematics

Wrap up your chapter revision by testing your knowledge against standard question formats. Everything on our platform is provided free of charge.

FAQs

Where can I access latest JEE Mathematics Matrices MCQs Set 17?

You can get most exhaustive JEE Mathematics Matrices MCQs Set 17 for free on StudiesToday.com. These MCQs for JEE Mathematics are updated for the 2026-27 academic session as per JEE examination standards.

Are Assertion-Reasoning and Case-Study MCQs included in the Mathematics JEE material?

Yes, our JEE Mathematics Matrices MCQs Set 17 include the latest type of questions, such as Assertion-Reasoning and Case-based MCQs. 50% of the JEE paper is now competency-based.

How do practicing Mathematics MCQs help in scoring full marks in JEE exams?

By solving our JEE Mathematics Matrices MCQs Set 17, JEE students can improve their accuracy and speed which is important as objective questions provide a chance to secure 100% marks in the Mathematics.

Do you provide answers and explanations for JEE Mathematics Matrices MCQs Set 17?

Yes, Mathematics MCQs for JEE have answer key and brief explanations to help students understand logic behind the correct option as its important for 2026 competency-focused JEE exams.

Can I practice these Mathematics JEE MCQs online?

Yes, you can also access online interactive tests for JEE Mathematics Matrices MCQs Set 17 on StudiesToday.com as they provide instant answers and score to help you track your progress in Mathematics.