The product of A = [(1, -2),(-3, 4)] and matrix M, AM = B where B = [(2), (24)], then the order of matrix M is ______.

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The product of A = [(1, -2),(-3, 4)] and matrix M, AM = B where B = [(2),(24)], then the order of matrix M is 2 $\times$ 1. Explanation: Let M be of order a $\times$ b. A is 2 $\times$ 2, so AM is defined only if the number of columns of A (2) equals the number of rows of M, hence a = 2. The product AM then has order 2 $\times$ b, but B is 2 $\times$ 1, so b = 1. Therefore, M is 2 $\times$ 1.

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