Let A=(1001)A = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}A=(1001) and B=(1001)B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}B=(1001) with det(A)=1\det(A) = 1det(A)=1 and det(B)=1\det(B) = 1det(B)=1. Compute det(A+B)\det(A + B)det(A+B).
det(A+B)=det(A)+det(B)=2\det(A+B) = \det(A) + \det(B) = 2det(A+B)=det(A)+det(B)=2
det(A+B)=4\det(A+B) = 4det(A+B)=4
det(A+B)=1\det(A+B) = 1det(A+B)=1
det(A+B)=0\det(A+B) = 0det(A+B)=0