Question

Prove that if a n*n matrix A has a row or column that is all 0's then the det(A) = 0

Answer 1

Each term of det A includes one factor that contains each row, hence each term has a zero factor. The sum of zeros is zero.

Answer 2

what about columns?

Answer 3

we can find the determinant by using columns also
or you can use the fact that the determinant remains unchanged when rows and columns are interchanged

Answer 4

hmm the det does change when you swap rows.

Answer 5

yes, it just changes in sign