Find the matrices of transformation `T_(1)T_(2) and T_(2)T_(1)` when `T_(1)` is rotated through an angle `60^(@) and T_(2)` is the reflection in the Y-asix Also, verify that `T_(1)T_(2)!=T_(2)T_(1).`

Explanation

`T_(1)=[(cos60^(@),-sin60^(@)),(sin60^(@),cos60^(@))]=[((1)/(2),-(sqrt3)/(2)),((sqrt3)/(2),(1)/(2))]=(1)/(2)[((1)/(sqrt3),-(sqrt3)/(1))]`
and `T_(2)=[(-1,0),(0,1)]`
`therefore" " T_(1)T_(2)=(1)/(2)[(1,-sqrt3),(sqrt3,1)]xx[(-1,0),(0,1)]=(1)/(2)[(-1+0,0-sqrt3),(-sqrt3+0,0+1)]`
`=(1)/(2)[(1,-sqrt3),(-sqrt3,1)]=[(-(1)/(2),(-sqrt3)/(2)),((-sqrt3)/(2),(1)/(2))]`
`T_(1)T_(2)=[(-1,0),(0,1)]xx(1)/(2)[(1,-sqrt3),(sqrt3,1)]=(1)/(2)[(-1+0,sqrt3+0),(0+sqrt3,0+1)]`
`=(1)/(2)[(-1,sqrt3),(sqrt3,1)]=[(-(1)/(2),(sqrt3)/(2)),((sqrt3)/(2),(1)/(2))]`
it is clear from Eqs. (i) and (ii) , then
`T_(1)T_(2)!=T_(2)T_(1)`