findvthe identity element of the binary operations * defined on a*b = ab^2
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Explanation:
i) Let e be an identity element & a×e=e×a⟹a
2
+e
2
=e
2
+a
2
.
∴ There is no possible value of e where a
2
+e
2
=e
2
+a
2
.
ii) Let e be an identity element & a×e=e×a⟹(a−e)
2
=(e−a)
2
⟹a
2
+e
2
−2ae=e
2
+a
2
−2ae.
There is no possible value of e where a
2
+e
2
−2ae=e
2
+a
2
−2ae.
iii) Let e be an identity element & a×e=e×a=a⟹ae
2
=ea
2
=a⟹ae(e−a)=0
∴e=0 or e=a.
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