Find matrices $A, B \in \mathbb{R}^{m\times n}$ such that $AB^T$ is orthogonal

Question

Is it possible to compute two matrices $A$ and $B$ $\in \mathbb{R}^{m\times n}$, with $m > n$, such that the product $AB^T$ $\in \mathbb{R}^{m\times m}$ is orthogonal and its columns are orthonormal?

Answer 1

Orthogonal matrices have full rank (they are invertible). The rank of $AB^T$ is at most $n$.