The set H of quaternions is defined as follows: -{[- H = c+di +di]: a,b,c,d€R}. a+bi -c+di a - bi Prove that H is a subr

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The Set H Of Quaternions Is Defined As Follows H C Di Di A B C D R A Bi C Di A Bi Prove That H Is A Subr 1 (70.05 KiB) Viewed 9 times

The set H of quaternions is defined as follows: -{[- H = c+di +di]: a,b,c,d€R}. a+bi -c+di a - bi Prove that H is a subring of M2x2(C). Then prove that H is a non-commutative ring with identity in which every nonzero element has a multiplicative inverse. (Such rings are called division rings or skew fields. They differ from fields only in the fact that their multiplication operation is not required to be commutative.)