Consider the matrix $A = (2 - 3 - 3 5)$ . Which of the following statements is true?

easy MCQ 1 mark Class 12 · Mathematics · Matrices

A is symmetric
A is skew-symmetric
A is orthogonal
A is singular

Answer

A is symmetric

The correct answer is A is symmetric — The matrix is not skew‑symmetric because $A_{ij} \neq = - A_{j i}$ , not orthogonal because $A A^{T} \neq = I$ , and its determinant $2 \cdot 5 - (- 3)^{2} = 10 - 9 = 1 \neq = 0$ , so it is not singular.

Step-by-step solution

A matrix is symmetric if $A_{ij} = A_{j i}$ for all $i, j$ .
Check the off‑diagonal entries: $A_{12} = - 3$ and $A_{21} = - 3$ , which are equal.
Since the diagonal entries are $2$ and $5$ , the matrix equals its transpose, so it is symmetric.
The matrix is not skew‑symmetric because $A_{ij} \neq = - A_{j i}$ , not orthogonal because $A A^{T} \neq = I$ , and its determinant $2 \cdot 5 - (- 3)^{2} = 10 - 9 = 1 \neq = 0$ , so it is not singular.

Common mistake: Confusing symmetric with skew‑symmetric (sign of off‑diagonal entries).

Concept tested: Symmetric matrix test

Published 29 August 2026 · How this solution was prepared and checked

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Step-by-step solution

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Consider the matrix $A = (2 - 3 - 3 5)$ . Which of the following statements is true?