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  4. If A is a symmetric matrix and n ∈ N, then An is

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

Matrices

Solution:

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