How do you do the reflection on y axis?

Don’t you change the X’s to their negatives and leave the Y’s alone?

e.g. [[1,2] [2,4]] => [[-1,2] [-2,4]] ?

This works:

It is like an identity matrix, except when you multiply by this matrix, it changes the sign of the ‘x’ axis values.

YES, the x coordinates of the vector becomes -ve whereas the the y coordinates remain the same in case of reflection about y axis…this is done by using the transformation matrix i.e [[-1,0] , [0,1]]