I have three questions for which I need help:

1/ Show that if a matrix has an inverse then it must be square.

2/ Let and B be square matrices such that AB = 0. Show that A cannot be invertible unless B = 0.

3/ Let B be an invertible matrix. If X and B are matrices such that AX = B, show that X = A-1B. Hence or otherwise, solve the system of equations:

2x - 3y = 1, 2x - 3y = 5

x + y = -4, x + y = 3

In question 3, where it says "X = A-1B", the '-1' is supposed to be inverted.