Linear algebra question Really need help asap and please sho

Linear algebra question. Really need help asap and please show any work necessary. Will give a good rating immediately! Thank you in advance!

4) (8 pts) Prove that the inverse of a symmetric nonsingular matrix, A, is symmetric.

Solution

Since A is symmetric,

A^T=A

Since A is nonsingular A^-1 exists. Now, we need to examine the transpose of A^-1

(A^-1)T= (A^T)^-1

=A^-1

since A^T=A

Thus A^-1 is symmetric, since it is equal to its own transpose.