I have a question over this problem that I've encountered. I don't know how to solve it.
Let $\ell$ be the line parametrized as $(t, 2t+1, 3t+2)$ and let $P$ be the plane with equation $x+y+z = 1.$ (a) Prove that the matrix $\mathbf{A} = \begin{pmatrix} -2 & -2 & 2 \\ 2 & 0 & 1 \\ 0& -1 & -1 \end{pmatrix} $maps all points on line $\ell$ to points on plane $P$.
(b) Prove that the matrix $\mathbf{B} = \begin{pmatrix} 1 & 1 & -1 \\ 3 & 3 & -1 \\ 5& 5 & -1 \end{pmatrix}$maps all points on plane $P$ to points on line $\ell$.
So far, I've tried just plugging points in and such, but it's not really a solid proof. Can someone help me please?
Edit 1: So far, I have transformed the parametrized line into a vector, to multiply the matrix with. However, I don't know how to move on.