Product symbol, order of multiplication if factors are not commutative?

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Regarding the product notation... if we have non-commutative things (for example matrices): $$\prod_{i=1}^N {\bf A}_i$$ Is it by default assumed to mean $${\bf A}_1{\bf A}_2\cdots {\bf A}_N$$ or $${\bf A}_N{\bf A}_{N-1} \cdots {\bf A}_1$$ or maybe even an arbitrary order?