Let A, B, C, and D be n × n matrices and x and y vectors in Rn. Prove following inequalities;
a. If A ≥ B ≥ O and C ≥ D ≥ O, then AC ≥ BD ≥ O.
b. If A > B and x ≥ 0, x ≠ 0, then Ax > Bx.