Question

Prove using the axioms of the determinant that det(A1 , ..., Aj , ..., Ak , ..., An ) = - det(A1 , ..., Ak , ..., Aj , ..., An ). That is, if you swap any two vectors in the determinant, then the magnitude stays the same but you get a sign change. Recall that this is a key observation that is used when performing row reduction (Gaussian Elimination).

Answer 1