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Operations on Matrices - Properties of Multiplication of Matrices

notes

The multiplication of matrices possesses the following properties, which we state without proof. 
1. The associative law For any three matrices A, B and C. We have (AB) C = A (BC), whenever both sides of the equality are defined.
2. The distributive law For three matrices A, B and C.
(i) A (B+C) = AB + AC
(ii) (A+B) C = AC + BC, whenever both sides of equality are defined.
3. The existence of multiplicative identity For every square matrix A, there exist an identity matrix of same order such that IA = AI = A.

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Shaalaa.com | Matrices part 26 (Property matrices multiplication)

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