A 2×2 matrix [[a, b], [c, d]] moves every point of the plane. Its columns say where the two unit arrows land: the across arrow [1, 0] lands on [a, c], the up arrow [0, 1] on [b, d], so the unit square becomes the parallelogram they span. Write area_change(matrix): how many times it multiplies area, negative if it flips the picture over.
| 2 | 0 |
| 0 | 3 |