Properties of Matrix Multiplication

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Associative Property of Matrix Multiplication
For any matrices A, B, and C, and scalar c, the following is true: (AB)C = A(BC)

Associative Property of Matrix Multiplication

For any matrices A, B, and C, and scalar c, the following is true:

(AB)C = A(BC)

Associative Property of Scalar Multiplication
For any matrices A, B, and C, and scalar c, the following is true: c(AB) = (cA)B = A(cB))

Associative Property of Scalar Multiplication

For any matrices A, B, and C, and scalar c, the following is true:

c(AB) = (cA)B = A(cB))

Left Distributive Property
For any matrices A, B, and C, and scalar c, the following is true: C(A + B) = CA + CB

Left Distributive Property

For any matrices A, B, and C, and scalar c, the following is true:

C(A + B) = CA + CB

Right Distributive Property
For any matrices A, B, and C, and scalar c, the following is true: A(B + C) = AB + AC

Right Distributive Property

For any matrices A, B, and C, and scalar c, the following is true:

A(B + C) = AB + AC