Which one among the following is correct?
(ba)−m = b−mam
Consider (ab)m,
(ab)m=ambm≠bmam
(ab)m=ambm [∵(xy)r=xryr] =am×b−m [∵1xn=x−n] ≠ambm
Consider (ba)−m,
(ba)−m=b−ma−m [∵(xy)r=xryr] =b−mam [∵1x−n=xn]
Consider (ab)−m,
(ab)−m=a−mb−m [∵(xy)r=xryr] =a−m×bm [∵1x−n=xn] ≠ambm
∴(ba)−m=b−mam