Matthews watched eagerly from the side of the arena, still blushing slightly from Rose's surprise hug. The way she and her Pokemon battled was truly amazing, they were perfectly in sync with strong attacks to boot. Matthew found himself watching her more than he watched the battle, absorbing every detail he could. There was something electrical in the air from the way she battled, something so amazing he he couldn't quite put it into words. All he knew was that he desperately wanted to see more of it. 

The match didn't take long, Roselia's type advantage over Brock's pokemon meant the battle was over shortly after it had begun and soon Mstthew found it was his turn to dash over and hug Rose.
"you guys were amazing!" He beamed, speaking in equal parts to Rose and Roselia "I mean, wow!" He probably would have gushed about the battle and how easy Rose made it look but Brock cut him off, suggesting that the two of them should travel together.

Instantly, Matthew was excited about the idea. In all of the stories he had read, trainers travelled in groups and he was eager to match that experience, but being a teenager, he didn't want to seem too eager.
"I uh, I mean, yeah. I'm going to Cerulean next, if you're heading that way... I mean, uh, I'd be okay with it." Matthew mumbled, blushing a little and looking at his shoes, as to hide the excitement glowing in his eyes. Hope elbowed him in the shins, making him yelp and look up "I mean, I would like that... And Hope would too"

So much of him still being in Kanto was thanks to Rose, she had ininvertedly saved Hope which in turn meant Matthew met Whirlygig, and since then she had been a decent person to have around. She always seemed to see good in darkness and it was infectious. But, of course, Matthew was more interested in her skill I'm battle. Matthew still had a lot to learn, and Rose seemed to be brimming with raw talent. If Matthew wanted to become champion someday, he would need to learn and he couldn't think of anyone better to learn from.