Inverse homogeneous transformation! - Programmers Heaven

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Inverse homogeneous transformation!

Hello, I have a question about inverse homogeneous transformation. while i am reading a book "Introduction to Robotics mechanics and control" there is an example which says that: We have two frames A and B, Frame A is deduced from A by rotating A 30 degree and translating it 4 by x and 3 by y so the matrix of the transformation of B relative to A is:
0.866 -0.5 0 4
0.5 0.866 0 3
0 0 1 0
0 0 0 1
The question is to find A relative to B so i said that the rotation will be -30 and the x=-4 and the y=-3 so it will be:
0.866 0.5 0 -4
-0.5 0.866 0 -3
0 0 1 0
0 0 0 1
but actually it is not the result they had a rule that changes the translation part(last column) by multiplying the matrix rotation of A relative to B by the translation vector and the result is inserted in the last column.
Please can any one help?
Hani Almousli......

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