M = [A, B; -B, A] where A is pxp symmetric pd and B is pxp skew-symmetric. When is M pd?

Question

Let M = [A, B; -B, A] be a 2p x 2p matrix where A is p x p symmetric positive definite (pd) real valued matrix and B is a p x p real valued skew-symmetric matrix. Also, the matrix A+iB is pd. Is the Matrix M always a pd? If not, under what conditions is M pd?

A trivial solution is when B is a zero matrix. It is of interest to investigate the sufficient conditions (if any) when B is not zero.

Note: M, by construction, is symmetric.