Requirements:
for matrices A (=lhs) and B (=rhs):
- the column number in A must match the row number in B
Properties
for matrices A, B, and C:
- not commutative: AB ≠ BA)
- associative: (AB)C = A(BC)
- left distributive: A(B + C) = AB + AC
- right distributive: (B + C)A = BA + CA
- multiplication by zero matrix yields zero matrix: A0 = 0A = 0