Please help with this question.

Prove the following statements: a) If A is a non-singular matrix, and k is a nonzero scalar, then kA is nonsingular and (kA)^-1 =k1A^-1.

b) If a matrix, A, has a row of zeros, it is singular. c) If a matrix, A, has a column of zeros, it is singular. d) Let A and B be square matrices such that AB=0 . A cannot be nonsingular unless

B=0. e) Is the sum of two nonsingular matrices necessarily nonsingular? Prove your answer.