An idempotent-matrix quadratic form in Mahalanobis coordinates gives a chi-square with rank-many degrees of freedom

Let $\underline X\sim N(\underline0,\Sigma)$ where $\Sigma$ is a $+$ve definite matrix, and A is an idempotent matrix of rank $k<P$. Let $Z=X^\top\Sigma^{-1}AX$. Then mean and variance of z respectively equal: