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.?

1 Answer
Jul 14, 2018

Please see the explanation below

Explanation:

The matrix of the reflection in the line #y=x# is

#A_1=((0,1),(1,0))#

The matrix of the rotation anticlockwise by #90^@# is

#A_2=((0,-1),(1,0))#

The combination of matrices #A_1# and #A_2# is

#A_2*A_1=((0,-1),(1,0))*((0,1),(1,0))#

#=((-1,0),(0,1))#

The matrix of the reflection in the y-axis is

#A_3=((-1,0),(0,1))#

Therefore,

#A_1*A_2=A_3#

For verification, you can take a vector #((x),(y))# and apply the matrices.