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Algebra Level 5

Let j:R2R2j: \mathbb{R^2} \rightarrow \mathbb{R^2} be the linear operator defined by (x,y)(x+2y,y)(x,y) \rightarrow (x + 2y, -y). If A=MatE(j)A = Mat_{E}(j) where E=E ={(1,0),(0,1)(1,0),(0,1)}. Find A-|A|.

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