From what I understand (please correct if I'm wrong) if I have an orthogonal 4x4 matrix that contains no scaling and only rotation and translation, I can obtain the inverse matrix by transposing the 9 rotation values and negating the translation values.

example:

11 12 13 x

21 22 23 y

31 32 33 z

0 0 0 1

becomes

11 21 31 -x

12 22 32 -y

13 23 33 -z

0 0 0 1

Is this true?

One more question:

If I multiply this inverse matrix by another matrix to get the relative tranform between the two original matrices, do I have to take out the translation vector first and then add it in after at the end?

Thanks for any help.