Show by using matrix method that a reflection about the line #y=x# followed by rotation about origin through 90° +ve is equivalent to reflection about y-axis.?
Reflection about the line
The effect of this reflection is to switch the x and y values of the reflected point. The matrix is:
#A = ((0,1),(1,0))#
CCW rotation of a point
For CCW rotations about origin by angle
#R(alpha) = ((cos alpha, - sin alpha),(sin alpha , cos alpha))#
If we combine these in the order suggested:
That is equivalent to a reflection in x-axis .
Making it a CW rotation:
That is a reflection in the y-axis.