If A = [a b] and B = [(c), (d)], then:

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KollegeApply · Accepted Answer

Both matrices AB and BA are possible. Explanation: A = [a b] has order 1 $\times$ 2 and B = [(c), (d)] has order 2 $\times$ 1. Since the number of columns of A(2) equals the number of rows of B(2), AB is defined and has order 1 $\times$ 1: AB = ac + bd. Also B(2 $\times$ 1) times A(1 $\times$ 2) is defined and gives a 2 $\times$ 2 matrix BA = [[ac, bc],[ad, bd]]. Because AB is a 1 $\times$ 1 scalar and BA is a 2 $\times$ 2 matrix, they are not equal in general. This follows from the usual rule for matrix multiplication product defined when cols (A) = rows (B).

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