Properties of matrix multiplication
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Matrix multiplication is not commutative
[Equation goes here - download the original to see it.] To show that [Equation goes here - download the original to see it.] is not generally true, we need a counter example. [Equation goes here - download the original to see it.] [Equation goes here - download the original to see it.] Of course, in some cases AB = BA, but these are exceptions, not the rule. You should be very aware of the failure of commutatively in Matrix multiplication. Multiplication of a matrix on the left is not equivalent to multiplication of a matrix on the right.
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Contents of Properties of matrix multiplication
1 Operations
2 Associativity of matrix multiplication 3 Matrix multiplication is not commutative
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