Question

If $A$ is skew-symmetric matrix and $n$ is odd 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 B skew-symmetric matrix

For a skew-symmetric matrix A, $A^T=-A.$
$(A^n{)}^T=(-1{)}^n{A}^n$, since n is an odd integer then $A^n$ is also a skew-symmetric matrix.