Effect of simple linear transformation Consider the linear transformation given by
$$T\left\{\begin{bmatrix}x \\y\\z\end{bmatrix}\right\} =\begin{bmatrix}-x\\y\\z\end{bmatrix}$$
Find a matrix $A$ such that $T(x) = Ax$, where x = $[x, y, z]^T$
My attempt: 
$$\begin{bmatrix}-1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1\end{bmatrix}$$
Describe in simple terms the effect of the linear transformation T on a three-dimensional image.
My attempt: 
Reflection along the x axis 
Is my inteprtretation correct?
 A: Let  $ E=\Bbb{R}^3$  equipped with a frame  (O; x, y, z), then we
speak about:
A reflection relatively to a plans (mirror) $P$.
Example: the transformation $\Bbb{A=}\left(
\begin{array}{ccc}
-1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}
\right) $indicates a reflection relatively to the plane (o, x, y).
One may ask, for example to find the matrix indicating a
reflection in any plane defined by the equation $ax + vy + cz = O$
  where $a,b,c$  are constants  in $\Bbb{R} $ not all null. (for
  the simplicity of the mirror , I have  imposed $O$ as element of the  mirror).
A rotation about an axis $\Delta$.
Example: the transformation $B=\left(
\begin{array}{ccc}
cos\theta & sin\theta & 0 \\
-sin\theta & cos\theta & 0 \\
0 & 0 & 1
\end{array}
\right) $indicates a rotation about the axis (O; z).
A similar issue is to find a matrix indicating the rotation about
any given
 straight line  $\Delta_ {(a, b, c)} = \{\lambda (a, b, c),\; \lambda \in \Bbb{R} \} $ where $(a, b, c)$
  is a non zero vector (for the simplicity, I chose  the rotation axis contain the origin $O$) .
On inversion relatively  to any point $M = (x 0, y_0, z_0)$.
For example, the transformation $C=\left(
\begin{array}{ccc}
-1 & 0 & 0 \\
0 & -1 & 0 \\
0 & 0 & -1
\end{array}
\right) $ indicating an inversion relatively  to the origin $O =
(0,0,0)$.
Again, a similar question is to find the matrix inversion
relatively  to any  given point $M=(x_0, Y_0, z_0)$ in the space
$\Bbb{R}^3$.
Thinks
