If a matrix A is an orthogonal matrix,
its column are already orthonormal vectors,
so, we don't need to change them using the Gram-Schmidt process to obtain column for Q.
So, we can take \(A=Q\)
now, we can find the matrix R from \(A=QR\) using the fact that if A orthogonal it is invertible.
So, QR factorization for an orthogonal matrix \(A=AI\).