Start with small matrices (1×1, 2×2, 3×3, ...), do the calculations by hand to gain some intuition, come up with a generalization to n×n matrices, prove it by i

Start with small matrices (1×1, 2×2, 3×3, ...), do the calculations by hand to gain some intuition, come up with a generalization to n×n matrices, prove it by induction.