Question

If $A$ is a square matrix of order $3$, then value of $|(A-A^T{)}^{2005}|$ is equal to

• A. $1$
• B. $3$
• C. $-1$
• D. $0$

Answer 1

The correct option is D $0$

Given,

$A$ is a square matrix of order$3$.

As we know

$A-A^T$ is skew symmetric matrix of order $3$.

$(A-A^T{)}^{2005}$ is skew symmetric matrix.

Since the determinant of sker symmetric matrix is $0$.

$\therefore |A-A^T{|}^{2005}=0$