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A triangle T whose vertices are A (2, 3), B (5, 3) and C (4, 1) is mapped onto triangle `T_1` whose vertices are `A_1` (4, 3), `B_1` (-1, 3) and `C_1` (x, y) by a transformation M = `((a,b),(c,d))`.
a) Find the: (i) Matrix M of the transformation. (ii) Coordinates of C1.
b) Triangle T2 is the image of triangle T1 under the reflection in the line y = x. find a single matrix that maps T onto T2.