Invariant Points FP1 - Please help!

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marinelife
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Currently studying FP1 with the OCR (MEI) board and have got stuck on a question involving invariant points and matrices. Here it is:

The matrix (3 -2)
..................(2 -1) represents a transformation, T. The inverse of transformation T is W.
i) Find the matrix representing W: Complete
ii) Show that TW=WT=I: Complete
iii) Find the invariant points for the transformation T: Complete, points on the line y=x

Then I get stuck on the next part:
iv) T is a shear. The line of shear is the line of invariant points for the shear. The factor of a shear gives the distance a point is moved as a multiple of its perpendicular distance from the line of shear. What is the factor of the shear T?

Please don't just tell me the answer, I need to know how to get there thank you!
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B_9710
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A point that is mapped to itself after a transformation is an invariant point so
T(x,y)=(x,y)
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marinelife
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(Original post by B_9710)
A point that is mapped to itself after a transformation is an invariant point so
T(x,y)=(x,y)
I did that part and got the line of invariant points to be y=x but I have no idea where to go from there
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