ROC-AUC = 0.9. What will happen to this metric if all model predictions are multiplied by 3?

ROC-AUC measures the quality of the ranking of the model's predictions, not their absolute values. Multiplying all predictions by the number 3 is a linear monotonic transformation that will not change the order of the predictions. Since ROC-AUC is based on comparing pairs of positive and negative examples by prediction order, the metric will remain unchanged and will still be 0.9.