Find matrix satisfying conditions

I'm looking to solve the following problem in matlab, but don't know which command to use.

Find a matrix B, s.t. A * B = I and 0 <= B*a <= b

Where A and B are matrices and a and b are vectors. I is the identity matrix.

Any idea what to use? (fsolve didn't work and I don't know how to formulate this in linprog)

Example:

A = [1 0 -1; 0 1 1];
a = [8; 6];
b = [15; 10; 10];