proud of," Clarke said.
"He's a wonderful guy, I really enjoy playing against him. He's a very good captain. He's always been a prize wicket for the Australian team and this test match is no different."
Cook repaid the compliments in kind.
"It's strange isn't it? How it's both captains in the same game," said Cook.
"He's obviously had an incredible career and he's been the leading batsman (in the world) for the last couple of years.
"We've had a fair few battles along the way, both of us, and he's one of these guys when you stop playing cricket you'll remember playing against him.
"It's great sharing it with him."
Where the pair would have differed before this series was in their relative success as captain, with Cook well ahead of his Australian rival.
That is not the only thing that has been turned around over the two tests in Brisbane and Adelaide and Cook admitted that his 100th test was probably the biggest challenge he has faced since becoming skipper.
Cook is the youngest player to reach a century of tests, having achieved the feat in just under eight years since his debut in early 2006.
He was not about to be drawn on whether he might one day match Sachin Tendulkar's record of 200 tests, which the Indian great recently sealed in his final match before retirement.
"Who knows? I've just got to cherish every one I play, I'm privileged to play a hundred and I hope to play a fair few more," Cook said.
"It would be wrong to presume anything but if people want me to play, I'll go on for as long as I can.
"(200 tests) is a long way away."