What a matrix does
A 2×2 matrix moves every point of the plane; its columns say where.
A 2×2 matrix is a rule that moves every point of the plane. It keeps the origin where it is, keeps straight lines straight and keeps parallel lines parallel.
You only need to know where two arrows go. The first column is where the unit arrow along x lands, the second column where the unit arrow along y lands. Every other point follows, because it is a mix of those two.
The unit square spanned by the two arrows becomes a parallelogram. Its area is the determinant: how much the matrix stretches or shrinks areas. A negative determinant means the plane was flipped over.
When the determinant is 0 the matrix flattens the plane onto a line. Different points land on the same spot, so the move cannot be undone: the matrix has no inverse.
Multiplying two matrices means doing one move after the other, which is why the order matters: rotating and then shearing is not shearing and then rotating.
Answer it first
A matrix has the columns (2, 0) and (0, 3). What does it do to areas?
Show the answer
It multiplies them by 6: it stretches by 2 along x and by 3 along y, and its determinant is 2·3 = 6.
Reading is not learning it
Leo teaches this at your pace, asks for your attempt before he shows his, and checks a week later what stayed.