Kubernetes : Cluster-Autoscaler: How to verify autoscaling is working
Actually cluster autoscaler checks for any unschedulable pods every 10 seconds and if any pods available in unschedulable state then it will check min and max of autoscaling group. You can check this wonderful FAQ how-does-scale-up-work of autoscaler. If it is not reached max then it will request to aws autoscaling group to add one more.
Now the answer of your question is, you can check or verify autoscaling easily by noticing whether you have any unscheduled pods in your cluster or not. If there is any then autoscaler will try to add one more node which will be reflected in autoscaler log if it is not reached in max limit.For more details you can check this FAQ. You can check also vertical pods scaler to get vertical pods scaling from here
You can tail the logs and see the events.
kubectl logs -f deployment/cluster-autoscaler -n kube-system --tail=10
It will show the scaling events.