CWMO 2018 Problem 3

Let $M = \{1,2,\cdots , 10\}$ , and let $T$ be a set of 2-element subsets of $M$ . For any two different elements $\{a,b\}, \{x,y\}$ in $T$ , the integer $(ax+by)(ay+bx)$ is not divisible by 11. Find the maximum size of $T$ .