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. In fact, it is already undecidable for sets of 6
matrices (or more) 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.