i) Matrix multiplication is not commutative in general.
i.e. AB ≠ BA
ii) Matrix multiplication is associative i.e.,
(AB)C = A(BC)
whenever both sides are defined.
iii) Matrix multiplication is distributive over matrix addition i.e.
(a) A (B + C) = AB + BC
(b) (A + B) C = AB + AC
Whenever both sides of equality are defined.
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