convexity of function of matrix

Question

Let $f(A,b)=y^T(I-aA)^{-1}b$ be a function of matrix $A$ and vector $b\geq 0$ such that all the elements of $A$ and $y$ are less than 1 and non-negative and $0<a<1$. Each row of $A$ sums up to 1.
Can someone please help me out to show that this is convex in $A$? I derived the gradient of $f$. But then no clue on how to compute the hessian. Any reference would also be very helpful.