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Symmetric Matrix

If A is n...

Question

If $A$ is $n$ squared matrix then $A A^{'}$ and $A^{'} A$ are symmetric.

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Solution

$(A A^{'})^{'} = (A^{'})^{'} A^{'} = A A^{'}$ and hence symmetric.
$(A^{'} A)^{'} = A^{'} (A^{'})^{'} = A^{'} A$ and hence symmetric.

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