Matrix as a transformationA = [0 3; 0 −2], det A = 0
original gridimage grid under Aimage of the unit square, area 0î ↦ (0, 0)ĵ ↦ (3, −2)
det A = 0: the two column vectors lie on one line. The unit square is flattened — the parallelogram degenerates to a segment with no area, and A is not invertible.