Question

Match each type of vector reflection with the matrix used to achieve it

Answer 1

Let us try reflecting (2,3) about x=y and across x-axis and y-axis.

If we are reflecting about y=x, that means both x,y values will be interchanged that is (2,3) will become (3,2)and this will be achieved by $\left[\begin{array}{cc}0&1\\1&0\end{array}\right]$ .

And for reflection across x-axis,y-value will be multiplied by -1.That is (2,3) becomes (2,-3) and the matrix used to achieve it is $\left[\begin{array}{cc}1&0\\0&-1\end{array}\right]$.

For reflection across y-axis, x-value will be multiplied by -1. That is (2,3) becomes (-2,3) when reflected across y-axis. The matrix used to achieve it will have -1 in the first place that is $\left[\begin{array}{cc}-1&0\\0&1\end{array}\right]$