Did Jesus keep the Sabbath when He walked the earth?

Jesus used the Sabbath day to announce His mission on Earth (Luke 4:16-19). In Isaiah 42:21, the prophet predicts that the Messiah would come to magnify the law, not to change it. In Matthew 24:20, Jesus alludes to the Sabbath in connection with future generations. Jesus also told his followers that He did not abolish that law:

Do not think that I came to destroy the law or the prophets, I did not come to destroy but to fulfill (Matthew 5:17 NKJV).
If you love Me, keep My commandments (John 14:15 NKJV).
For I am the LORD, I change not (Malachi 3:6)