Linear Algebra · Lesson 4
Matrix Multiplication
Matrix multiplication is not entry-by-entry — it uses the dot product of rows with columns. The result encodes composed transformations, and the order matters: AB ≠ BA in general.
Quick Check
1. To multiply A·B, which must be true about dimensions?
A and B must be square
Columns of A = Rows of B
Rows of A = Rows of B
A and B must be the same size
2. A is 3×2 and B is 2×5. What is the size of AB?
2×2
3×5
5×3
3×2
3. For 2×2 matrices, which is generally true?
AB = BA always
AB ≠ BA in general
AB = A+B
AB is always symmetric
4. (AB)ᵀ equals:
AᵀBᵀ
BᵀAᵀ
ABᵀ
AᵀB