Question

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

• A. skew symmetric
• B. symmetric
• C. identity
• D. idempotent

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.