Short Quiz

Question 1 of 5

CBSE Board Exam 2025

Which of the following can be both a symmetric and skew-symmetric matrix?

A Unit Matrix B Diagonal Matrix C Null Matrix D Row Matrix

Select one option. Answers are shown after the test.

Question 2 of 5

CBSE Board Exam 2026

If a square matrix A is such that \(\mathrm{A}^{2}=\mathrm{A}\) and \((\mathrm{I}-\mathrm{A})^{3}=\mathrm{xA}+\mathrm{I}\), then value of \(x\) must be :

A 7 B 5 C -7 D -1

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Question 3 of 5

CBSE Board Exam 2025

If A and B are square matrices of same order, then \(\left(\mathrm{AB}^{\mathrm{T}}-\mathrm{BA}^{\mathrm{T}}\right)\) is a

A symmetric matrix B skew-symmetric matrix C null matrix D unit matrix

Select one option. Answers are shown after the test.

Question 4 of 5

CBSE Board Exam 2024

For any square matrix A , (A \(-\mathrm{A}^{\prime}\) ) is always

A an identity matrix B a null matrix C a skew symmetric matrix D a symmetric matrix

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Question 5 of 5

CBSE Board Exam 2024

If \(A=\left[a_{i j}\right]\) is an identity matrix, then which of the following is true ?

A \(\quad \mathrm{a}_{\mathrm{ij}}= \begin{cases}0, & \text { if } \mathrm{i}=\mathrm{j} \\ 1, & \text { if } \mathrm{i} \neq \mathrm{j}\end{cases}\) B \(\quad \mathrm{a}_{\mathrm{ij}}=1, \forall \mathrm{i}, \mathrm{j}\) C \(\quad a_{i j}=0, \forall i, j\) D \(\quad a_{\mathrm{ij}}= \begin{cases}0, & \text { if } \mathrm{i} \neq \mathrm{j} \\ 1, & \text { if } \mathrm{i}=\mathrm{j}\end{cases}\)

Select one option. Answers are shown after the test.

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