Why do we have different way in multiplication in matrices?
I think you may be referring to the fact that A*B usually gives a different result to B*A with matrix multiplication. This means that you have to be careful when multiplying both sides of an equation that you do left multiplication on both sides or right multiplication on both sides as appropriate. Example. Suppose A, B, C are square matrices and you know that A*B = C then A*B*B’ = C*B’………………………B’ is inverse of B A = C*B’……………………….because B*B’ = I and A*I = A However it would have been wrong to say A*B*B’ = B’*C as you would be doing left multiplication one side and right multiplication on the other.
