Question

If $A$ is a skew symmetric matrix, then $A^2$ is a

Answer 1

Given that $A$ is skew- symmetric matrix
So $A^{{}^{\prime }}=-A$
$\text{Now}{\left(A^2\right)}^{{}^{\prime }}={\left(A^{{}^{\prime }}\right)}^2[\therefore {\left(A^{{}^{\prime }}\right)}^n={\left(A^n\right)}^{{}^{\prime }}]$
$\Rightarrow {\left(A^2\right)}^{{}^{\prime }}=(-A{)}^2[\text{Using equation (1)}]$
$\Rightarrow {\left(A^2\right)}^{{}^{\prime }}=A^2$
If $A^{{}^{\prime }}=A$, then $A$ is called symmetric matrix.
$\Rightarrow A^2$ is symmetric matrix.