Determine whether the given map [tex]\varphi[/tex] is an isomorphism of the first binary structure with the second. < M2(R ), usual multiplication > with <R, usual multiplication> where [tex]\varphi[/tex](A) is the determinant of matrix A. The determinant of the matrix is ad-bc, so [tex]\varphi[/tex](A)=ad-bc. For this to be an isomorphism, I have to show that the function is one to one, onto and preserves the operations. I'm having trouble getting this to work. Any suggestions?