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 $$A^{-1}A=I$$?