Let A= (2, -2; 1, -1) and B= (-1, 2; -1, 2). Then the number of elements in the set {(n, m): n, m ∈{1,2, … …., 10}. and.n A^n+m B^m=I} is \ \ \ \.

Let $\displaystyle A=\left(\begin{array}{ll}2 & -2 \\ 1 & -1\end{array}\right)$ and $\displaystyle B=\left(\begin{array}{ll}-1 & 2 \\ -1 & 2\end{array}\right)$. Then the number of elements in the set $\displaystyle \left\{(n, m): n, m \in\{1,2, \ldots \ldots ., 10\}\right.$ and $\displaystyle \left.n A^n+m B^m=I\right\}$ is \_\_\_\_.