In computer science, the matrix mortality problem (or mortal matrix problem) is a decision problem that asks, given a finite set 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[1].
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[3], and for sets of matrices which contain at most one invertible matrix[4].
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