Question

the matrix $\left[\begin{array}{ccc}0&1\\1&0\end{array}\right]$ is the reflection in the line 
A) x-y = 0  (B) x+y = 0  (C) x-y = 1  (D) x+y =1..  And tell me mathod how can i do it ?

Answer 1

Apply the given matrix as a transformation function to coordinates of a point P(x,y). Multiply matrix with coordinates vector to get a new coordinate vector.

$\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}y\\x\end{array}\right]$

If x = y, then there is no change in the coordinates of the given point. That means x = y is a mirror for other points.

So x becomes y and y becomes x after transformation. Take (3,0) and (0,3) join them. Take (2,0) and (0,2) join them. You find that.

This is the reflection along the diagonal of matrix: x = y or x - y =0

See the diagram.