Matrix Multiplication Is Composition

Multiply matrix A by matrix B and you're not doing arithmetic — you're doing composition. The product is a single new matrix that performs B's transformation and then A's, in one step.

Try it mentally: rotate 90°, then mirror the plane — the combined warp is some skewed flip, and the product matrix encodes it exactly. The entries are just bookkeeping for where the basis arrows land after both moves.

One catch: A×B reads right-to-left — B happens first. And it matters.