Let be $Q$ a matrix with eigenvalues less 1. If I multiply each row for a number very near 1, then the matrix still have all his eigenvalues less 1

Question

Let be $Q$ a matrix with eigenvalues less than 1. Let be $Q_f$ a matrix definided by $$Q_f(i,j)=f(i)Q(i,j).$$ I need to prove that for $f$ enough near 1, then $Q_f$ have only eigenvalues less than 1.