[Math] Image of the unit square under linear transformation

Question

Let $\mathbf{B} = \begin{pmatrix}1&-1 \\ 3 & -2\end{pmatrix}.$ The
image of the unit square in $\mathbb{R}^2$ under the linear mapping
$T_{\mathbf{B}}: \mathbb{R}^2 \to \mathbb{R}^2$ defined by
$T_\mathbf{B}{\mathbf{x}} = \mathbf{Bx}$ is

(A) a square; (B) a non-square rectangle; (C) a non-rectangular
parallelogram; (D) a line segment; (E) the point $(1, −2)$; (F) none of
these.

I think it takes $(0,0) \mapsto (0,0)$, $(1,0) \mapsto (1,3)$, $(0,1) \mapsto (-1,-2)$, and $(1,1) \mapsto (0,1)$. Is this right? I can't figure out what shape it should be.

Answer 1

Here is an image of the unit square image: