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[Solved] Consider the linear transformation T: R^2 * 2 \rightarrow R^2 * 2

Question: Consider the linear transformation \(T: \mathbb{R}^{2 \times 2} \rightarrow \mathbb{R}^{2 \times 2}\)

\[T(M)=\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right] M-M\left[\begin{array}{ll} 1 & 1 \\ 1 & 1 \end{array}\right]\]

Write the matrix of \(T\) with respect to the basis

\[\left[\begin{array}{cc} 1 & 1 \\ -1 & -1 \end{array}\right],\left[\begin{array}{ll} 1 & -1 \\ 1 & -1 \end{array}\right],\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right],\left[\begin{array}{ll} 0 & 1 \\ 1 & 0 \end{array}\right]\]

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