How to use private key and public key with chain i

问题:

I'm facing with a problem with mutual ssl authentication. I have generated a csr and a private key, I gave the csr to the our customer CA that signed it and gave me back the certificate/public key with the a chain inside. When I try to communicate with the server that require mutual SSL , using that certificate chain and my private key I have an error because the private key does not match the certificate. I'm using postman to do the call and I'm using openssl to verify the modulus :

openssl x509 -noout -modulus -in certificate.pem
openssl rsa -noout -modulus -in privateKey.key
openssl req -noout -modulus -in csr.csr

The last two match but the first one no. If I extract the single certificate from the chain the modulus will match but the resulting certificate, without chain, is not a trusted certificate but a self-signed one. What I'm loosing, what I'm doing wrong? I'm sure there is something missing.

THanks to all.