Question

If A is a skew–symmetric matrix of order 3, then the matrix $A^4$ is

• A. Skew symmetric
• B. Symmetric
• C. Diagonal
• D. None of those

Answer 1

The correct option is B Symmetric

$Wehave{A}^T=-A$
$(A^4{)}^T=(A.A.A.A{)}^T=A^T{A}^T{A}^T{A}^T$
$\Rightarrow (-A)(-A)(-A)(-A)$
$=(-1{)}^4{A}^4=A^4$