I've got the following I'm trying to prove and want to make sure my proof is sound.
Let $A$ be an $n\times n$ matrix, prove $A^{-1}$ orthogonal.
Proof
a square matrix is said to be orthogonal if its transpose is the same as its inverse, that is if $$ A^{-1}=A^{T} $$ thus, $$ (A^{-1})^{-1}=A=(A^{T})^{T}=(A^{-1})^{T} $$ So by definition, $A^{-1}$ is orthogonal. []
Any suggestions on how to make this better would be great.