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the product AB is not defined since A and B are not conformable with respect to multiplication.

918 APPENDIX B: RUDIMENTS OF MATRIX ALGEBRA

Properties of Matrix Multiplication

1. Matrix multiplication is not necessarily commutative; that is, in general, AB = BA. Therefore, the order in which the matrices are multiplied is very important. AB means that A is postmultiplied by B or B is premultiplied by A.

2. Even if AB and BA exist, the resulting matrices may not be of the same order. Thus, if A is M x N and B is N x M, AB is M x M whereas BA is N x N, hence of different order.

3. Even if A and B are both square matrices, so that AB and BA are both defined, the resulting matrices will not be necessarily equal. For example, if

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