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.