If the coefficient of $x^7$ in $\big(ax^2+\large\frac{1}{bx}\big)^{11}$ is equal to coefficient of $x^{-7}$ in $\big(ax-\large\frac{1}{bx^2}\big)^{11}$, then $a$ and $b$ satisfy the relation

Question

$\begin{array}{1 1} a+b =1 \\ a-b =1 \\ ab=1 \\ \frac{a}{b}=1 \end{array}$