Question

If A is a square matrix $A+A^T$ is symmetric matrix, then
$A-A^T=$

• A. Unit matrix
• B. Symmetric matrix
• C. Skew symmetric matrix
• D. Zero matrix

Answer 1

The correct option is C Skew symmetric matrix

$(A-A^T{)}^T=A^T-(A^T{)}^T=A^T-A[\because (A^T{)}^T=A]=-(A-A^T)$
So, $A-A^T$ ​is a skew symmetric matrix.