There is an important feature of orthogonal matrix that
$AA^T = A^TA = I$
meaning that
$A^{-1}=A^T$
It makes inverse operation very cheap.

University of Michigan - Ann Arbor

A matrix is orthonormal matrix if and only if its rows are mutually orthonormal and its columns are mutually orthonormal as well.

Linear Algebra - orthogonal matrix

Goodfellow, I., Bengio, Y., & Courville, A. (2016). $\mathit{Deep \ Learning.}$ MIT Press. Retrieved from [www.deeplearningbook.org](https://www.deeplearningbook.org) 

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