If $P'AP$ is a spectral decomposition of a symmetric matrix $A$ then prove that $A$ is positive definite iff $P'AP$ also positive definite.

Question

If $P'AP$ is a spectral decomposition of a symmetric matrix $A$ then prove that

$A$ is positive definite iff $P'AP$ also positive definite.

definition:

A matrix $A$ is said to be positive definite if for all non-zero $x$, $x'Ax>0$.