What 3 by 3 matrices represent the transformations that
a) project every vector onto the $x-y$ plane?
b) reflect every vector through the $x-y$ plane?
c) rotate the $x-y$ plane through 90 degrees, leaving the z-axis alone?
d) rotate the $x-y$ plane, then $x-z$, then $y-z$, through 90 degrees?
I am very confused as to how to approach these problems. When dealing with just 2x2 matrices, I know that the rotation matrix is just $\begin{bmatrix} cos\theta & -sin\theta\\ sin\theta&cos\theta \end{bmatrix}$, and if I wanted to rotate something onto the $x$-axis, I would let $\theta =0$ and the transformational matrix would just be $\begin{bmatrix} 1 & 0\\ 0&1 \end{bmatrix}$. The 2 by 2 projection and reflection matrices $\begin{bmatrix} c^{2} & cs\\ cs&s^{2} \end{bmatrix}$, $\begin{bmatrix} 2c^{2}-1 & 2cs\\ 2cs&2s^{2}-1 \end{bmatrix}$, respectively. But when the 3rd dimension is introduced, I don't know how to approach these problems anymore. Could anyone walk me through this?