Q:

square matrices A and B have equal rows/colomns and A*B = I matrix does that mean that B*A also = I?

If you have two square matrices with equal rows and columns A and B and AB = the identity matrix does that mean that BA also equals the identity matrix?

A:

By the definition of the inverse, if
$$AB = I,$$
Where $I$ is the identity matrix,
This means that $B = A^{-1} \wedge A = B^{-1}$. If
$$BA \neq I \implies BB^{-1} \neq I \implies B \neq B,$$
which is a contradiction. Thus, $BA = I.$ And so $AB = I \implies BA = I.$

