A widely used method for estimating eigenvalues of a general matrix A is the QR algorithm. Under suitable conditions, this algorithm produces a sequence of matrices, all similar to A, that become almost upper triangular, with diagonal entries that approach the eigenvalues of A. The main idea is to factor A (or another matrix similar to A) in the form A = Q₁R₁, where Q^T_I = Q_I^-1 and R₁ is upper triangular. The factors are interchanged to form A₁ = R₁Q₁, which is again factored as A₁ = Q²R²; then to form A² = R²Q², and so on. 

Show that if A = QR with Q invertible, then A is similar to A₁ = RQ.