If a, b are elements of a ring and m, n∈Z, show that (na)(mb)=(mn)(ab)

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unett · Accepted Answer

We have to show that if a, b∈R and m,n∈Z, then (na)(mb)=(nm)(ab). Notice that  (na)(mb)=(a+....+a)(b+....+b)n×m×=a(b+...+b)+...+a(b+...+b)ms=  (ab+...+ab)+...+(ab+...+ab)m×n×=m(ab)+...+m(ab)n×=(nm)(ab)  Hence the proof.

If a, b are elements of a ring and m, n∈Z, show that (na)(mb)=(mn)(ab)

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