I'm having difficulty with this linear transformation puzzle, I'd be grateful if you could give it a go. I haven't quoted my textbook verbatim, so if there is any confusion please let me know and I'll restate it. Thanks

Referring to the image below, the triangle t is undergoing a number of reflections

A(t) = 1

B(t) = 2

C(t) = 3

BC(t) = 4

(i) Show that operations AB and BA are the same

(ii) Describe the combined operation BC geometrically.

(iii)Simplify C(CB), (CC)B and BC(CB)...using I to denote the identity operation.

(iv) Obtain expressions, as combinations of A, B and C for operations which carry

(a) t to x

(b) t to y

(c) x to t