# Determine an unknown matrix

General question:
How do you determine a matrix B when given A and AB?

## Answers and Replies

If you know the inverse of A, you can multiply on the left side by A^-1 to get B, i.e. (A^-1)AB = B.

Oh I see. I understand the computation, but could you explain the theory behind this?

This isn't exactly a thorough explanation, but basically if you multiply a matrix by its inverse, you get the identity matrix I. If you multiply any matrix by the identity matrix, you get the original matrix back again, e.g. IA = AI = A.

HallsofIvy