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For each nonnegative integer $k$, you could find the possible tuples of matrices $(A_1, ..., A_k)$ as follows:
for each of
-1,0,1, find the ways to write it as a sum of $k$ summands each in {-1,0,1}.the target matrix $M$ has $n^2$ entries $m_{i, j}$; so the $(A_1, ..., A_k)$ are obtained by combining all the possible ways to get each entry.
