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Let A be a non-singular matrix. Show th...

Let `A` be a non-singular matrix. Show that `A^T A^(-1)` is symmetric if `A^2=(A^T)^2`

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First let `A^T A^−1` be symmetric. Then
`(A^TA^−1)T=A^TA^−1`
`⇒(A^−1)^T(A^T)^T=A^TA^−1`
`⇒(A^T)^−1A=A^TA^−1 [∵(A^−1)^T=(A^T)^−1]`
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