I am reading a proof of the property $\det (A\cdotp B) = \det (A) \cdotp \det (B)$. It starts by defining $f(A)=\det (A \cdotp B)$. Then it states "We shall first prove that $f$ satisfies the elementary row properties of the determinant function.
As $f$ is the determinant function, is it not obvious that it satisfies the elementary row properties?