MAT006 · Matrices & determinants · Classes 11–12
Matrix multiplication
To multiply matrices, each element of AB is a row of A times a column of B (multiply pairs and add). The columns of A must equal the rows of B, and in general AB ≠ BA.
ABMatrix multiplication
📐 Formula
(AB)ᵢⱼ = Σₖ aᵢₖ bₖⱼ
✏️ Worked example
[1 2; 0 1] × [1 2; 3 4] = [1·1 + 2·3, 1·2 + 2·4; 3, 4] = [7 10; 3 4].
🌍 Where it is used
Transformations in graphics, networks, economics models.
❓ Quick check
(2 × 3) times (3 × 4) gives order…
🏋️ Practice
Easy[1 0; 0 1] × [5 6; 7 8]?
Answer: [5 6; 7 8]
Medium[1 2] × [3; 4]?
Answer: [11]
ChallengeIs AB always equal to BA?
Answer: No