When we perform these operations:
Ri+αRj Determinant does not change
αRi Determinant multiplies by
αRi⇔Rj Determinant multiplies by (-1)
I know these are true, however, I'm looking for proofs for each of them. They aren't anywhere in my lecture notes and I can't find anything online, all I can find is what happens to the determinant, not the actual proof.
Has anyone got anything that could help? Thank you