## determinants of matrices [closed]

Given that $A$ is an invertible square matrix and $AA^T = A^TA = I$. Suppose that $B=A^{-1}A^T$ and $det A$ is not equal to $det B$. Show that $det (A+B) =0$.

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This is phrased like a homework problem. I voted to close. – Angelo Jul 16 at 9:57