Let R be a commutative ring with unity and M2(R) the ring of 2 2 matrices with entries from R. Show that A E M2(R) is a unit if and only if det (A) is a unit in Hint: There is a nice way to find the inverse of a 2 2 matrix. Hint 2: You may want to use that det(AB) = det(A) det(B) ) Find the units of M2(Z2)