Let $T : \mathbb R^2 \to \mathbb R^2$ be the linear map that assigns to each point in $\mathbb R^2$ its reflection along the $x$-axis.
My questions:
What is the determinant of $T$?
What is trace of $T$ ?
My try:
My answer was the determinant is $2$ and trace is zero, i.e., I take $(1,1)$ and its reflect image on $x$-axis is $(1,-1)$. Is my answer correct? Thanks for any suggestions.
Since $T(1,0)=(1,0)$ and $T(0,1)=(0,-1)$, the matrix of $T$ with respect to the canonical basis is $\left(\begin{smallmatrix}1&0\\0&-1\end{smallmatrix}\right)$. Therefore, the trace is $0$ and the determinant is $-1$.