Question

If $A$ is a symmetric matrix and $n\in N$, then $A^n$ is

• A. symmetric matrix
• B. a diagonal matrix
• C. a skew-symmetric
• D. None of the above

Answer 1

The correct option is A

symmetric matrix

Explanation for the correct option:

$A^T=A$ [$\because$$A$ is symmetric matrix]

$\Rightarrow$$\begin{array}{rcl}{\left(A^n\right)}^T& =& {\left(A^T\right)}^n\\ & =& A^n\end{array}$

$\mathbf{\therefore }{\mathit{A}}^{\mathbf{n}}$ is a symmetric matrix.

Hence, Option ‘A’ is Correct.