Thank you for sharing the image. I see a mathematical problem involving transformations $S$ and $T$. Let me help by extracting the details and solving the problem step by step.

Part (a)

• Matrix Representation: The transformation $S \cdot T$ is represented by a $2 \times 2$ matrix, where the unknowns are marked as "?" in matrix $S$.

We need to:

1. Provide an example for $[T]$ and $[S]$, ensuring that $[S]$ is not the identity matrix.

Part (b)

The question refers to:

1. $R_{\frac{\pi}{2}}: \mathbb{R}^2 \to \mathbb{R}^2$: Counterclockwise rotation by $\frac{\pi}{2}$.
2. $S_0$: Reflection of $S$ in the $x$-axis.
3. $S_1$: Reflection of $S$ in the line $y = x$.

The tasks involve:

1. Finding $S_0$, $S_1$, and $R_{\frac{\pi}{2}} \cdot S_0$, using the results of (a).

Would you like me to begin with detailed calculations for (a), (b), or both? Let me know your preference.