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transformation in coordinate plane, (a,b) ->(a + b, b), (a, b)-> (-b, a)

Source: KJMO 2006 p4

May 1, 2019
analytic geometrygeometric transformationtransformationtransformationsalgebra

Problem Statement

In the coordinate plane, de fine M={(a,b),a,b∈Z}M = \{(a, b),a,b \in Z\}. A transformation SS, which is de fined on MM, sends (a,b)(a,b) to (a+b,b)(a + b, b). Transformation TT, also de fined on MM, sends (a,b)(a, b) to (−b,a)(-b, a). Prove that for all (a,b)∈M(a, b) \in M, we can use S,TS,T denitely to map it to (g,0)(g,0).
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