Let $$A = \left( {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right)$ and $B = \left( {\matrix{ { - 1} & 2 \cr { - 1} & 2 \cr } } \right)$. Then the number of elements in the set {(n, m) : n, m $\in$$ {1, 2, .........., 10} and nAn + mBm = I} is ____________.

Question

Let $$A = \left( {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right)$ and $B = \left( {\matrix{ { - 1} & 2 \cr { - 1} & 2 \cr } } \right)$. Then the number of elements in the set {(n, m) : n, m $\in$$ {1, 2, .........., 10} and nAⁿ + mB^m = I} is ____________.

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