Question: Let $A ∈ M_n(F)$ be a matrix whose columns form an orthonormal basis for $F$ $n \times 1$ under the dot product.
Show $A$ is invertible and the inverse of $A$ is $A^∗$.
Attempt: Showing $A$ is invertible is trivial enough since its columns form an ON basis, but my class hasn't touched on adjoints much, so I am not sure how to proceed to show that $A^{-1} = A^*$.