A matrix is a rectangular table of numbers. Matrices of the same size add entry by entry and a scalar multiplies every entry. A product takes a row of the first times a column of the second, so AB and BA can differ. The zero and identity matrices act like 0 and 1. A 2 by 2 matrix moves every point of the plane, its determinant is the area factor, and when the determinant is not zero the matrix has an inverse that solves a system written as A[x; y] = b.