Answer
See solution
Work Step by Step
U is a square matrix whose columns are orthonormal and linearly independent. U is also invertible with $U^{-1}=U^T$.
The rows of U, which are the columns of $U^T$ are orthonormal because $(U^T)^{-1}=(U^{-1})^T=(U^T)^T$. The inverse is equal to the transpose, so $U^T$ is an orthogonal matrix and its columns, which are the rows of U, form a basis for $R^n$.
