Binary operations and their propertiesAQA A-Level Further Maths: Mind map

Exam questions on Binary operations and their properties

1. The binary operation $\ast$ is defined on the set of real numbers by $a\ast b=2a+3b$.
   Show that $\ast$ is not associative.2 marks
2. The binary operation $\otimes$ is defined on the set $\{0,1,2,3,4,5\}$ by $x\otimes y=$ the remainder when $xy$ is divided by 6, that is multiplication modulo 6.
   Prove that $\otimes$ is commutative.2 marks
3. The binary operation $\circ$ is defined on the set $S=\{1,2,3,4\}$ by $a\circ b=$ the remainder when $ab$ is divided by 5.
   Construct the Cayley table for $\circ$ on $S$, with the first element of $a\circ b$ given by the row.3 marks