Let's say I have 2 $n$ by $n$ matrices called $A$ and $B$. If I flip $A$ left to right, then up and down, and do element-wise multiplication with matrix $B$ and sum up the elements of this new matrix, is that the same as flipping $B$ left to right, up and down, and then doing element-wise multiplication with matrix $A$ and then computing the sum? How can I prove this? Examples show it's true, but looking for a proof.
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