# Special Types of Matrices

hkus10
1) show that if AB = AC and A is nonsingular, then B = C.

2) show that if A is nonsingular and AB = 0 for an n x n matrix B, then B = 0.

3) Consider the homogenous system Ax=0, where A is n x n. If A is nonsingular, show that the only solution is the trivial one, x=0.

4) Prove that if A is symmetric and nonsingular, then A^-1 is symmetric.

Thanks