Find the matrix representation $A$ of a linear mapping $T$ : $\mathbb R^2 \to \mathbb R^2$ that rotates points $\pi$ radians clockwise, then reflects points through the line $x_2 = - x_1$. Determine the range of $T$. Determine if $(1,1)$ is in the range of $T$. Determine if this linear mapping $T$ is invertible by calculating the determinant of $A$.
Alright, I've been trying to solve the following problem for nearly 3 hours now, but no avail. I don't even fully understand the question. I didn't find any tutorials online that met my needs. I'd appreciate if someone could go through the solution with (brief if possible) explanation of the problem.