Matrices – Positive definitivity of the matrix.

I need to prove that the matrix. $ M $ it's positive defined I know that $ R, P $ is positive defined, but I can not imagine how to simplify this expression to prove $ M succ 0 $. Some help would be very appreciated.

$ M = A ^ TPB big ((B ^ TPB + R) ^ {- 1} – (B ^ TPB + R) ^ {1} B ^ TPB (B ^ TPB + R) -1 big) B ^ TPA A, P in mathbb {R} ^ {n times n}, ; B in mathbb {R} ^ {n times m}, ; R in mathbb {R} ^ {m times m}, ; ; R, P succ0, ; ; R, P ; symmetric $