Pitfall 1: det(kA) = k * det(A) WRONG. Correct: det(kA) = $k^n$ * det(A). This appears in 1-2 questions per year.

Pitfall 2: AB = 0 implies A = 0 or B = 0 WRONG. Matrices can have zero products without being zero. Example: A = [[1,0],[0,0]], B = [[0,0],[1,0]], AB = 0.

Pitfall 3: Confusing adj(A) with cofactor matrix Adjoint = TRANSPOSE of cofactor matrix. Missing the transpose changes the answer completely.

Pitfall 4: Forgetting sign in cofactors $C_{ij}$ = (-1)^(i+j) * $M_{ij}$. The alternating sign is missed under exam pressure.

Pitfall 5: Cramer's Rule when D = 0 Cramer's Rule gives unique solution ONLY when D != 0. When D = 0, you must separately analyze D1, D2, D3.

Pitfall 6: Skew-symmetric determinant for even order det = 0 only for ODD order skew-symmetric matrices. For even order, det can be non-zero (it equals the square of the Pfaffian).

Exam strategy: After solving, spend 15 seconds checking: (1) Did I use $k^n$ not k? (2) Did I transpose for adjoint? (3) Is the sign correct on cofactors?