Matrix A: m rows × n cols

↳A = [[1,2],[3,4]] is 2×2

Add: same dimensions only

↳[[1,2]] + [[3,4]] = [[4,6]]

Multiply A(m×n) × B(n×p) = C(m×p)

↳A(2×3) × B(3×4) → C(2×4)

Identity I: 1s on diagonal, 0s elsewhere

↳I₂ = [[1,0],[0,1]]; AI = A

Determinant 2×2: ad − bc

↳|[[2,3],[1,4]]| = 8 − 3 = 5

Inverse: A⁻¹A = I

↳A⁻¹ exists iff det ≠ 0