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Consider a binary operation on Q -{1} define by a*b =a+b-ab (i) Find the identity element in Q-{1} (ii) Show that each a in Q-{1} has its invese |
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Answer» `a*e=a rarr a+e-ae=a` `rarr e(1-a=0 rarr e=0` [before a `ne` 1] `therefore` 0 is the identity element (II) Let a in Q-{1} be an arbitray element and let b be its INVERSE Then `a*b=0 rarr a+b-ab=0 rarr ab-b=a` `rarr b(a-1)=a rarr b=(a)/(a-1)` Thus each a in Q-{1} has `(a)/(a-1)` as its inverse |
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