Unable to ssh into ec2 instance: WARNING: UNPROTECTED PRIVATE KEY FILE! Permissions 0555 for '.pem' are too open

After I created an ec2 instance, I tried to ssh into the port by using the private key, but even though I chmod the key down to 400, I get this error.

vagrant@ubuntu-bionic:/vagrant$ chmod 400 ./itmo-544-2019.pem
vagrant@ubuntu-bionic:/vagrant$ ssh -i ./itmo-544-2019.pem ubuntu@<ip-address>
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
@ WARNING: UNPROTECTED PRIVATE KEY FILE! @
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
Permissions 0555 for './itmo-544-2019.pem' are too open.
It is required that your private key files are NOT accessible by others.
This private key will be ignored.
Load key "./itmo-544-2019.pem": bad permissions
ubuntu@18.205.191.197: Permission denied (publickey).

I made sure the private key starts with

-----BEGIN RSA PRIVATE KEY-----

and ends with

-----END RSA PRIVATE KEY-----

I also tried chmod 600 ./itmo-544-2019.pem. But this didn't help either.

Any idea why?

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