Question

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

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

Answer 1

Answer: (A)

Since, $A$ is symmetric $\Rightarrow A^{\prime }=A$.
Now, ${\left(A^n\right)}^{\prime }={\left(A^{\prime }\right)}^n=A^n$
$\text{Therefore,}{A}^n$ is a symmetric matrix.