Trap 1: det(kA) = k * det(A) -- WRONG Correct: det(kA) = $k^n$ * det(A). Appears 1-2 times per year.

Trap 2: AB = O implies A = O or B = O -- WRONG Matrices can multiply to give zero without either being zero. This defies scalar algebra intuition.

Trap 3: AB = AC implies B = C -- WRONG Cancellation requires A to be invertible (det(A) != 0). Singular A allows non-trivial B-C in its null space.

Trap 4: det(A + B) = det(A) + det(B) -- WRONG Determinant is multiplicative, not additive. This is a fundamental distinction from scalar operations.

Trap 5: Adjoint vs Cofactor matrix adj(A) = (cofactor matrix)^T. The transpose step is frequently forgotten.

Trap 6: Skew-symmetric determinant = 0 always -- WRONG for even order Only TRUE for odd order. Even order skew-symmetric matrices can have non-zero determinants.

Trap 7: D = 0 implies infinite solutions -- INCOMPLETE D = 0 means either infinite solutions OR no solution. Must check $D_i$ values for the complete picture.

Trap 8: Cramer's Rule when D = 0 -- INAPPLICABLE Cannot divide by zero. Use rank method or $D_i$ analysis instead.

Exam Strategy Checklist:

1. Before final answer: Did I use $k^n$ (not just k) for det(kA)?
2. Did I transpose the cofactor matrix for adjoint?
3. For systems with D = 0: Did I check ALL $D_i$ values?
4. For skew-symmetric: Is the order odd or even?
5. Am I assuming commutativity? (AB != BA generally)