155 Define an operation * on the set $\{(x, y) \mid x, y \in \mathbf{R}\}$ as follows:
$\left(x_{1}, y_{1}\right) *\left(x_{2}, y_{2}\right)=\left(x_{1} x_{2} \cdot x_{1} y_{2}+x_{2} y_{1}\right)$, if for any $(x, y)$ there is $(x$, $y) *(a, b)=(x, y)$, then $(a, b)=$ $\qquad$
$155(1,0)$. Take $(x, y)=(1,1)$, it is easy to see that $(a, b)=(1,0)$. It is not hard to verify that it satisfies the conditions.