Science:Math Exam Resources/Courses/MATH221/December 2019/Question 02 (e)/Statement

In each case, either give an example or state that no such example exists (you don’t have to explain why not).

The matrix $A$ of a linear transformation $T:\mathbb {R} ^{2}\to \mathbb {R} ^{2},$ different from the identity, such that the two sets

$$\left\{{\begin{bmatrix}0\\2\end{bmatrix}},\;{\begin{bmatrix}1\\0\end{bmatrix}}\right\},\;\;\left\{T\left({\begin{bmatrix}0\\2\end{bmatrix}}\right),\;T\left({\begin{bmatrix}1\\0\end{bmatrix}}\right)\right\}$$

are equal.