Multiply two matrices of compatible dimensions with full row-by-column working.
Matrix multiplication computes (AB)ᵢⱼ as the dot product of row i of A with column j of B. The number of columns in A must equal the number of rows in B. The result is an m×n matrix when A is m×p and B is p×n. Matrix multiplication is not commutative in general.
Matrix Multiplication
(AB)ᵢⱼ = Σₖ Aᵢₖ · Bₖⱼ
No. In general AB ≠ BA. The dimensions may not even permit the reverse product.
Multiplying any matrix A by the identity I gives A back: AI = IA = A.