with problem with matrices, reflections, rotations

[dellatorre]

Looking for help with a problem I'm working on:

"Show that matrix
[0 -1 0]
[-1 0 0]
[0 0 1]
for a reflection about line y=-x
is equivalent to a reflection relative to the y-axis followed by a counter-clockwise rotation of 90 degrees."

So for my answer, first I have for the reflection relative to the y axis, I have the matrix:
[-1 0 0]
[0 1 0]
[0 0 1]

and for the counter-clockwise rotation of 90 degrees, I have the matrix:
[0 -1 0]
[1 0 0]
[0 0 1]

but then I don't know what my next step should be.

Can anyone help me with this?

thanks,
Della

 

[Dick]

Sure. The matrix of the combined operation is the product of the matrices for the individual operations. Multiply (matrix of rotation)*(matrix of reflection).

 

[dellatorre]

thank you