Question 1: Consider the determinant as a function from the space of 2x2 real matrices to the real numbers. Is it a linear transformation? Question 2: Let A,B,C,D be 2x2 real matrices. Then in block form create the matrix E=[ A B \\ C D] (which means the entries of A go in the upper left, the entries of B go in the upper right, the entries of C go in the lower left, the entries of D go in the lower right). So E is a 4x4 matrix. Do you think that det(E)=det(A)det(D)-det(B)det(C) ?
