Question

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

• A. symmetric
• B. skew-symmetric
• C. null matrix

Answer 1

The correct option is A symmetric

Since, A is skew symm.
$A^T=-A{\left(A^2\right)}^T={\left(A.A\right)}^T=A^T.A^T=\left(-A\right)\left(-A\right)=A^2\therefore \mathrm{Symm}.{\left(A^4\right)}^T={\left(A^2.A^2\right)}^T={\left(A^2\right)}^T.{\left(A^2\right)}^T=A^2.A^2=A^4\therefore \mathrm{Symm}.$