math1081-assignment/q2/b.md

Part B

Is \star symmetric?

For \star to be symmetric, every set of elements (x_1,x_2)\in\Q^2,(y_1,y_2)\in\Q^2 which satisfies (x_1,x_2)\star(y_1,y_2) must also satisfy (y_1,y_2)\star(x_1,x_2).

Assume (y_1,y_2)\star(x_1,x_2) is true. This means that y_1 x_2 =y_2 x_1, which is the same as as x_{1}y_{2}=x_{2}y_{1} (i.e. the original relation). Therefore the requirement is satisfied, and \star is symmetric.