Let $T:\mathbb{R}^{2}\to\mathbb{R}^{2}$ be the linear transformation that first reflects a vector about the line $y=x$, then rotates the result $90^{\circ}$ counter‑clockwise, and finally scales the vector by a factor of $3$. Find the standard matrix of $T$ and state its determinant.

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\begin{pmatrix}-3&0\0&3\end{pmatrix}; determinant = -9

Neco 2025 Further Mathematics Question 10

Let \(T:\mathbb{R}^{2}\to\mathbb{R}^{2}\) be the linear transformation that first reflects a vector about the line \(y=x\), then rotates the result \(90^{\circ}\) counter‑clockwise, and finally scales the vector by a factor of \(3\). Find the standard matrix of \(T\) and state its determinant.

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