Anyone good with matrices

Given two matrices A and B where neither is square, what conditions need to exist so that AB exists and BA exists?

Thanks so much!

They must by m by n and n by m, where m,n are any unequal positive integers.

Let matrix A have dimensions m x n and matrix B have dimensions s x t.

For AB to exist, then n = s. For BA to exist, then m = t.


So for both AB and BA to exist matrix A must be m x n and matix B must be n x m.