If a * b = 10ab on Q^{+},then find the invers | vedclass

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(A) Let $e$ be the identity element for the operation $*$.By definition,$a * e = a = e * a$.Given $a * b = 10ab$,we have $10ae = a$.Since $a \in Q^{+}

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(A) Let $e$ be the identity element for the operation $*$.By definition,$a * e = a = e * a$.Given $a * b = 10ab$,we have $10ae = a$.Since $a \in Q^{+}$,$a 
eq 0$,so $10e = 1$,which gives $e = \frac{1}{10}$.Let $a^{\prime}$ be the inverse of $0.01$.By definition,$0.01 * a^{\prime} = e$.Substituting the values,$10 	imes 0.01 	imes a^{\prime} = \frac{1}{10}$.$10 	imes \frac{1}{100} 	imes a^{\prime} = \frac{1}{10}$.$0.1 	imes a^{\prime} = 0.1$.Therefore,$a^{\prime} = 1$.

If $a * b = 10ab$ on $Q^{+}$,then find the inverse of $0.01$.

Similar Questions

Let $^$ be a binary operation on the set $Q$ of rational numbers defined as $a \,^\, b = a b^{2}$. Determine whether the operation is commutative and associative.

For each binary operation $^$ defined below,determine whether $^$ is commutative or associative. On $Z^+$,define $a ^* b = a^b$.

Determine whether or not each of the definitions of $$ given below gives a binary operation. In the event that $$ is not a binary operation,give justification for this. On $Z^{+}$,define $$ by $a b = a$.

Show that none of the operations given above has an identity element.

State whether the following statement is true or false. Justify: For an arbitrary binary operation $^$ on a set $N$,$a \,^ \,a = a$ for all $a \in N$.

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