Identity and inversesAQA A-Level Further Maths: Mind map

Exam questions on Identity and inverses

1. The binary operation $*$ is defined on the set of real numbers $\mathbb{R}$ by $a*b=a+b-3$.
   Find the element of $\mathbb{R}$ that is its own inverse.2 marks
2. The binary operation $\circ$ is defined on the set of real numbers $\mathbb{R}$ by $a\circ b=\frac{ab}{4}$.
   Explain why the element $0$ has no inverse in $\mathbb{R}$ under $\circ$.2 marks
3. The set $S=\{1,2,3,4,5,6\}$ under the operation $\otimes$, multiplication modulo 7.
   Show that $1$ is the identity element and find the inverse of each element of $S$.3 marks