Question 4.3.3: Let T: R²→R² be the mapping of Example 1 with T (v) = Av, wh...

Introduction to Linear Algebra with Applications

Let T: R²→R² be the mapping of Example 1 with T (v) = Av, where

$A = \begin{bmatrix} 1&0 \\ -1&0 \end{bmatrix}$

Verify that the inverse map $T^{-1}$ :R² → R² is given by $T^{-1}$ (w) $= A^{-1}$ w, where

$A^{-1} = \begin{bmatrix} 0&-1 \\ 1&1 \end{bmatrix}$

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