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- An element $e \in N $ is an identify element for operation * if $a \ast e=e \ast a$ for all $a \in N$

Given $ a *b =a^2+b^2$

Let e be an identity element of * operation

By definition of identity element we have a*e=e*a = a

but by definition of * operation $ a *e =a^2+e^2$ =>$ a=a^2+e^2$ =>$ e^2= a-a^2$

=> e = square root of$ a=a^2$, but square root of $a=a^2$ does not always belong to N for all a in N

Therefore the operation * defined by $ a *b =a^2+b^2$ has no identity.

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