Finding the number of elements of order $2$ in a given group 
How many elements of order $2$ are there in the group of order $16$ generated by $a$ and $b$ such that $o(a)=8$ and $o(b)=2$ and $bab^{-1}=a^{-1}$?

The basic thing i do not understand is that order of the generator must be equal to the order of the group. So how can $a$ and $b$ in this case generate the given group ?
I tried something like this, as $b$ is of order $2$ it must be its own inverse. So from the given condition on $a$ and $b$ replacing $b$ by $b^{-1}$ i get that $o(ba)=2$ . SO there are at least two elements of order two. However, this answer is obviously not good enough.

Hint: Consider $ba^{j}ba^{j}$ for $0 \leq j \leq 7.$
