Matrix mortality problem


In computer science, the matrix mortality problem is a decision problem that asks, given a set of size m of n×''n matrices with integer coefficients, whether the zero matrix can be expressed as a finite product of matrices from this set.
The matrix mortality problem is known to be undecidable when n'' ≥ 3. In fact, it is already undecidable for sets of 6
matrices when n = 3, for 4 matrices when n = 5, for 3 matrices when n = 9, and for 2 matrices when n = 15.
In the case n = 2, it is an open problem whether matrix mortality is decidable, but several special cases have been solved: the problem is decidable for sets of 2 matrices, and for sets of matrices which contain at most one invertible matrix.
n\''m''123456
2✅✅
3✅✖️
4✅✖️
5✅✖️✖️✖️
...✅✖️✖️✖️
9✅✖️✖️✖️✖️
...✅✖️✖️✖️✖️
15✅✖️✖️✖️✖️✖️