Problem15:Let A be a symmetric matrix.

Recall the definition of a symmetric matrix.
A matrix is symmetric if it equals its transpose.
We also need the following simple properties,

> ;
2 T 2 T T T (2 A  3 A + I) = 2 (A )  3 A + I
and since A, A^2 and I are symmetric, 
> ;
2 T 2 (2 A  3 A + I) = 2 A  3 A + I