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

We are given that the matrix A is skew symmetric which implies that,
$A^T=-A$ --------(1)
$(A^4{)}^T=(A.A.A.A.{)}^T=A^T{A}^T{A}^T{A}^T$ (By applying the property of transpose of a matrix)
$\Rightarrow$ (-A) (-A) (-A) (-A) (Using equation (1))
$=(-1{)}^4{A}^4=A^4$
i.e, $(A^4{)}^T=(A^4)$
$A^4$ is symmetric.