Please Help 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

CliffLee

I thought someone would have an answer by now.

shabiakhan

Dear Della.,,

ur ans is with me... may be it mite help u or it mite be 2 late ....
Still let me tell u

its actually thye concatenation of the two matrices ie Multiplivation . But keep in mind the order of concatenation.

Lme show u 2d Reflection

[0 -1] . [-1 0]
[1 0] [0 1]

[0 -1]
[-1 0]