The title above is actually the matrix of the transformation I was looking for and corresponds the a 90° rotation and a vertical flip... it also corresponds to a 270° rotation and a horizontal flip.
Anyway, I've spent so long trying to figure it out using any number of egg boxes that I managed to lose sight of why I was trying to transform the array... I guess that it's because I hard-coded the elements of the array in its initial iteration and wanted the new non-hard-coded to be in the same format... whereas it doesn't have to be...
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