At 9:25 of that lecture Mumshad is talking about the Ansible ‘authorized_keys’ module; however, I believe the module is ‘authorized_key’ (i.e. no ‘s’). (I noticed this given the last lab in the previous section of the course required you to fix a bunch of errant playbooks and I recalled having to fix that in one of them.)
I checked the Ansible docs and it would seem that the module is in fact ‘authorized_key’ (latest Ansible docs link):
You might want to double-check it and update the presentation if so.
Excellent course by the way, I’m really enjoying it!