Calculation:

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 \(A=Q\)

Step 2

now, we can find the matrix R from \(A=QR\) using the fact that if A orthogonal it is invertible.

\(A=QR=AR\)

\(\Rightarrow A^{-1}A=A^{-1}AR=R\)

\(\Rightarrow R=I\)

So, QR factorization for an orthogonal matrix \(A=AI\).