Matrices by hand

Determinant, inverse, products and eigenvalues, with every entry worked out. About 10 minutes, A-level / University.

What you will do

1. A matrix is a recipe. A matrix is a grid of numbers that acts on points. Its determinant tells you how it scales area.
2. The inverse. The inverse undoes the matrix. Swap the diagonal, negate the others, divide by the determinant.
3. Multiplying matrices. Each entry is a row of the first times a column of the second. Order matters.
4. Eigenvalues. Eigenvalues are the numbers λ with (A - I) = 0: the stretch factors along special directions.
5. A 3 by 3 determinant. Expand along the top row with alternating signs.