The boundedness of all products of a pair of matrices is undecidable

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The generalized spectral radius and extremal norms (2002, background): “As the question whether a pair of matrices is product bounded is undecidable by a recent result of Blondel and Tsitsiklis [26] we do not expect to obtain an easily checkable criterion and so our condition is just sufficient but not necessary.”
Corrigendum/addendum to: Sets of matrices all infinite products of which converge (2001, unknown): “The PFA EMPTINESS problem has been shown to be undecidable, see [4] for a discussion and references.”
Approximation of the joint spectral radius using sum of squares (2007, background): “Blondel and Tsitsiklis have shown that computing ρ is hard from a computational complexity viewpoint, and even approximating it is diﬃcult [BT00a, TB97].”