Aspire Faculty ID #17371 · Topic: CUET MCA 2026 · Just now
CUET MCA 2026

A matrix is both symmetric and skew symmetric matrix

(a) A is diagonal matrix

(b) A is zero matrix

(c) A is scalar matrix

(d) A is square matrix

Solution

If a matrix A is symmetric, then
AT = A

If a matrix A is skew symmetric, then
AT = −A

For both conditions to hold:
A = −A

⇒ 2A = 0
⇒ A = 0

Therefore, the matrix must be a zero matrix.

Correct Answer: (b) A is zero matrix

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