Composition of Reflection Is a Rotation? Prove that if $T_{1},T_{2}$ are reflections in lines through O then $T_{1}\circ T_{2}$ is a rotation about O. Once again, a hint would be preferable to an answer. I'm not fami...--prophetes.ai

Composition of Reflection Is a Rotation? Prove that if $T_{1},T_{2}$ are reflections in lines through O then $T_{1}\circ T_{2}$ is a rotation about O. Once again, a hint would be preferable to an answer. I'm not familiar with these types of linear transformations, as I am not accustomed to thinking of them as functions. Thanks in advance for everyone who answers.

Since you requested a hint, go ahead and think of the transformations as matrices, and treat composition as multiplication. Otherwise, think about how reflection changes chirality, but two reflections would leave chirality unchanged.