Faith is defined as as the act of believing in things not observed.

Paul tells us that God's faith was justified when His Son, as the human Jesus, sacrificed Himself on the "cross", and  God's righteousness is revealed through the faith of Jesus.

Now, how God could be anything but righteous, I don't know?  

Righteousness is defined as the status of being justified.  How could God not be justified in any action He undertakes?

But, what it means, I believe, is that by Jesus being obedient to the Father unto death and thus sacrificing Himself for all of God's people, then Jesus' faith makes known to us the righteousness of God..     

Jesus , after much agonizing as any human would, in the garden of Gesthemane, justified God's faith when he willingly sacrificed himself so that all mankind would be saved, and His faith in God was justified by His resurrection.  

He knew of the promise of the resurrection, when he sacrificed Himself, and His return to eternal life justified His faith.

Paul assures us that the believer's faith that, Jesus died for our offenses and was resurrected  because of our justifying, brings righteousness to us, as well.  We live in this faith, and will live in the promised resurrection on the basis of Jesus Christ's faith..paulnbob