It's important to remember that matrix multiplication is not commutative. That is, if [A] and [B] are matrices, then
[A]x[B] is not necessarily equal to [B]x[A] . In fact, it's possible that the matrix product [A]x[B] could be a matrix, and that the matrix product [B]x[A] is not a matrix.
Matrix multiplication "logic" in solving systems is indicated below. This should make sense to you.
The key here is that if you are solving systems of equations involving 2 or more variables, [A]-1x[B] will be a matrix, but [B]x[A]-1 will not be a matrix. To repeat, matrix multiplication is not commutative.
MATH POWER TO ALL.