I’m currently in my first year of studies (mathematics); today while the professor was explaining Binet’s Theorem and its consequences i thought the following:
Let $A'\in M_n(K)$ be the matrix obtained as a result from reducing some $A\in M_n(K)$; is it always true that $\det A|\det A'$?
It seems almost trivial to me given the multi-linear and alternating nature of the determinant (which I believe to have understood) but I’m not completely sure.