For matrix $A_{n\times n},X_{n\times p}$, $rank(X)=p$. Prove that if $M(X)\subset M(A)$, $X^TAX>0$.

Question

Since $M(X)\subset M(A)$, I know that there exist a matrix B, s.t. $X=AB$.

Since $rank(X)=p$，I know that X is full rank, which means $Xy=0$ only has zero solution.

But I don't know how to complete the proof.