Linear Alg.: Let A be a symmetric nonsingular matrix. Prove

[buckaroobill]

Okay so I was practicing proofs and the following appeared in my book. i'm confused as to how do it so i would be thankful for any help:

Let A be a symmetric nonsingular matrix. Prove that its inverse (A^-1) is symmetric.

 

[pka]

If the matrix $\displaystyle A = \left[ {a_{jk} } \right]_{n \times n}$ is symmetric then you must realize that for each pair $\displaystyle \left( {j,k} \right)\quad \Rightarrow \quad a_{jk} = a_{kj} .$ What does that mean about cofactors and hence about the inverse?