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## Homework Statement

if [itex]L_A: ℝ^n -> ℝ^n : X-> A.X [/itex] is a linear transformation, and A is an orthogonal matrix, show that L_A is an isomorphism.

also given is that [itex] (ℝ,ℝ^n,+,[.,.]) [/itex] , the standard Euclidian space which has inproduct [X,Y]= X^T.Y

## Homework Equations

ortogonal matrix, so [itex]A^T=A^{-1}[/itex]

isomorphism = bijective and linear (so what is left to show is bijective)

## The Attempt at a Solution

don't know where to start