Let F be a field. R is an element of Mat(2,2) [a -b b a] for a, b in F with matrix operations. a. Show that R is a commutative ring with 1 and the set of diagonal matrices are naturally isomorphic to F . b. For which of the fields Q , R , C , F5 , F7 is R a field? c. Characterize which elements of R have a multiplicative inverse. d. Characterize the fields F for which R will be a field. e. For which Fp ( p prime) is R a field?