Let A = {0, 1, 2, 3, 4, 5, 6}. If a, b in A,a | vedclass

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(C) The operation $a * b$ is defined as the remainder when $ab$ is divided by $7$,where $a, b \in A$.First,we find the identity element $e \in A$ such

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$4$

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(C) The operation $a * b$ is defined as the remainder when $ab$ is divided by $7$,where $a, b \in A$.First,we find the identity element $e \in A$ such that $a * e = a$ for all $a \in A$.This means the remainder of $ae$ divided by $7$ is $a$.For $a \in \{1, 2, 3, 4, 5, 6\}$,$a * 1 = 	ext{remainder of } (a 	imes 1) / 7 = a$.Thus,the identity element $e = 1$.To find the inverse of $2$,we need an element $x \in A$ such that $2 * x = e = 1$.This means the remainder of $(2 	imes x)$ divided by $7$ is $1$.Testing values from $A$:$2 * 1 = 2$$2 * 2 = 4$$2 * 3 = 6$$2 * 4 = 8 \equiv 1 \pmod{7}$Since $2 * 4 = 1$,the inverse of $2$ is $4$.

Let $A = \{0, 1, 2, 3, 4, 5, 6\}$. If $a, b \in A$,and $a * b$ is defined as the remainder when $ab$ is divided by $7$,then find the inverse of $2$ under the operation $*$.

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