In the above example, AB is
defined but BA is not defined because B has 3 column while A has only 2 (and not 3)
rows If A, B are, respectively m × n, k × l matrices, then both AB and BA are defined
if and only if n = k and l = m In particular, if both A and B are square matrices of the
same order, then both AB and BA are defined Non-commutativity of multiplication of matrices
Now, we shall see by an example that even if AB and BA are both defined, it is not
necessary that AB = BA