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If A and B are non-singular symmetric matrices such that `AB=BA`, then prove that `A^(-1) B^(-1)` is symmetric matrix.

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We have `AB=BA`
Now, `(A^(-1) B^(-1))^(T)=((BA)^(-1))^(T)=((BA)^(T))^(-1)`
`=(A^(T)B^(T))^(-1)=(AB)^(-1)=(BA)^(-1)=A^(-1)B^(-1)`
Thus, `A^(-1) B^(-1)` is symmetric matrix.
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