Take $A=B=I_2$, which are <invertible matrices>. Then $\det(A+B)=\det(2I_2)=4$, whereas $\det A+\det B=2$. This proves that the <determinant is not additive>. Being a <multilinear map> of separate columns does not imply additivity in the entire <matrix>.

Solution

Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2003 / Paper 1 / 5 / b / i / Solution

 Solution (source code)