Matrix multiplication

An m × n matrix can multiply an n × p matrix, giving an m × p result. The inner dimensions must match. Matrix multiplication usually does not commute, so AB and BA may differ or only one may be defined.

For a point written as a column vector, a 2 × 2 transformation matrix acts on its left. AQA 8365 calculations are restricted to 2 × 2 or 2 × 1 matrices. Determinants and inverse matrices belong to other mapped courses, not this specification requirement.

Worked example

Multiply [[1,2],[3,4]] by [[2],[−1]].

1. First entry: 1 × 2 + 2 × (−1) = 0.
2. Second entry: 3 × 2 + 4 × (−1) = 2.

Answer: [[0],[2]]