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[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 fi eld.

e. For which Fp

( p prime) is R a field?