Private or public key is not of ec algorithm

1. Which algorithm is used for public private key encryption?
2. How do I know if my private key and certificate match?

Which algorithm is used for public private key encryption?

Public Key Cryptography (asymmetric) uses encryption algorithms such as RSA and Elliptic Curve Cryptography (ECC) to create the public and private keys.

How do I know if my private key and certificate match?

Compare the output from both commands. If they are identical then the private key matches the certificate. In this example the private key matches the certificate.