Proof of R Transpose and Inverse Equals Identity Matrix

[GuitaristOfRa]

Looking over a proof of something, I was confused at this step:

We end up with: R^{T} R = I (the identity matrix)
This must mean that R^{-1} = R^{T}

This is confusing me because I know that A A^{-1} = I , but in the R case the transpose is on the left side instead of the right, and it seems to me that it matters what order the matrices are multiplied.

 

[homology]

Okay, start with AA^{-1}=I. Can you turn this into A^{-1}A=I?