Question

Show that the matrix $KA$ is symmetric or skew symmetric according as $A$ is symmetric or skew symmetric.

Answer 1

$(KA{)}^{\prime }=K{A}^{\prime }=KA$ if $A$ is symmetric
$\therefore$ $KA$ is symmetric
$(KA{)}^{\prime }=K{A}^{\prime }=K(-A)=-KA$ if $A$ is skew symmetric.
$\therefore$ $KA$ is skew symmetric.