Is multiplication comutitive in numbers
I.e
Is N×M equal M×N?? Where N and M any numbers
And why??
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Of course not. $N\times M=M\times N^2$. – Matt Samuel Nov 13 '19 at 19:04
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For quaternions no, since for example $ij=-ji$, but for fields $K$ yes, because the group $(K^{\times},\cdot)$ is commutative. – Dietrich Burde Nov 13 '19 at 19:06
1 Answers
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It depends what you mean by "numbers". Complex numbers commute, as do special cases thereof, such as integers. However, quaternions don't in general commute, so nor do more inclusive systems such as the octonions.
J.G.
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@user479750 As I said, $\Bbb Z\subseteq\Bbb Q\subseteq\Bbb R\subseteq\Bbb C$ ensures these sets all commute, but $\Bbb H$ doesn't. – J.G. Nov 14 '19 at 10:10