Yes, you can use induction on $n$ to prove:
$P(n)$: If there are $n$ participants in a knockout tournament, then $(n-1)$ matches will be needed to declare a champion.
Base case(s): Is $(P(1)$ true? Sure: $P(1)$ If there is only one team ($n=1$), then no matches are needed $(n-1 = 1-1=0),$ because by default, the one team that showed up for the tournament is the champion.
$P(2)$ : If there are $n=2$ teams, then ($(n-1)= 2-1 =1$) matches are needed to determine a champion. Of course, exactly one match (team A vs team B) is needed to determine the champion.
Assume $P(n)$ is true.
Now show that, given $P(n)$, $P(n+1)$ must therefore hold, meaning the following must be proven true, given $P(n):\;\;$
"If there are $n+1$ teams, then $((n+1) - 1)= n$ matches are needed to determine the champion.