How to succinctly express $A_k{\times}A_{k-1}{\times}A_{k-2}{\times} ... {\times}A_1$

Question

I was thinking of writing: $$\prod_{i=k}^1 A_i$$ But I'm not sure if it is the correct way to do it.

As in: $$\left(A_1{\times}A_2{\times}A_3{\times} ... A_k\right)^{-1} = A_k^{-1}{\times}A^{-1}_{k-1}{\times}A^{-1}_{k-2}{\times} ... {\times}A^{-1}_1$$

I intended to write it more succinctly as: $$ \left(\prod_{i=1}^k A_i \right)^{-1} = \, \prod_{i=k}^1 A_i^{-1}$$

But I'm not sure if it's the correct way of representing it.  
 
 
 
 
 
 
 
 

EDIT

The $A_i$ are matrices.

Answer 1

Depends on what the object $A_j$ is, but you could use a big $\times$ with limits. See here.

E.g:

Answer 2

It's probably understandable, but not common, to have the indices for the product go in the reverse order. Instead, it would be more common to change the formula for the factors to fix things. You can write something like the following: $$\left(\prod_{i=1}^kA_i\right)^{-1}=\prod_{i=1}^kA^{-1}_{k+1-i}$$

As an aside, if you were worried about the use of $\displaystyle{\prod}$ for the product of matrices, it's in use on Wikipedia, for instance.