Question: abstract algebra Problem 8 Let C be the set R x R with the usual coordinatewise addition and a new multiplication given by (a, b)(c,

abstract algebra

Problem 8 Let C be the set R x R with the usual coordinatewise addition and a new multiplication given by (a, b)(c, d) = (ac - bd, ad + bc). Under these operations, R x R is a field. (a) (15 points) Find the multiplicative identity of C and show that every nonzero element (a, b) has a multiplicative inverse in C. (b) (15 points) Prove that CC

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