Given the following matrices A and B, find an invertible matrix U such that UA = B:

A and B must be invertible, we have UA=B, since A is invertible. A^-1 exists, by multiplying with A^-1, we have UA A^-1 = B A^-1. But AA^-1 = I (identity matrix) and XI=X, for all matrix X, we find UI = B A^-1, and U = B A^-1.