Question

If $A$ is skew-symmetric matrix and $n$ is even positive integer, then $A^n$ is

• A. a symmetric matrix
• B. skew-symmetric matrix
• C. diagonal matrix
• D. triangular matrix

Answer 1

The correct option is A a symmetric matrix

If A is skew symmetric or symmetric matrix then $A^2$ is a symmetric matrix.
$A^n=(A^2{)}^{n/2}$
n is even.
$\therefore A^n$ is symmetric matrix.
$\because A$ is a skew symmetric matrix.