Exercise 14.6. Let R = C.1+C · i + C · j +C · k, where the addition and the multiplication laws of R are extended from the Hamilton quaternion algebra, i.e. 1, i, j, k satisfy 1 · a = a = a· 1, Va € R, i2 = j2 = k2 = −1, ij = k = − ji. Show that R is isomorphic to M2(C). (Hint: consider the extension of the ring homomorphism from H into M2(C).)

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