Question

If $A$ is a square matrix, then $A-A^{\prime }$ is a

• A. Diagonal matrix
• B. Skew-symmetric matrix
• C. Symmetric matrix
• D. None of these

Answer 1

Answer: (B)

Skew-symmetric matrix

Given $A$ is square matrix

$A-A^T$ is which kind of matrix

${(A-A^T)}^T=A^T-{\left(A^T\right)}^T$

$=A^T-A$

$=-(A-A^T)$

$\because {(A-A^T)}^T=-(A-A^T)$

$\therefore A-A^T$ is a skew symmetric matrix

Option B is correct