In many practical applications, we are interested in computing the product of given matrices and/or a power of a given matrix. In some cases, the initial matrices are only known with interval uncertainty. It turns out that under this uncertainty, there is a principal difference between the product of two matrices and the product of three (or more) matrices:
on the one hand, it is more or less known that the problems of computing the exact range for the product of two matrices -- and for the square of a matrix -- are computationally feasible;
on the other hand, we prove that the problems of computing the exact ranges for the product of three matrices -- and for the third power of a matrix -- are NP-hard.