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Explained very well, May i know what is Multicollinearity problem ?

I think the binary justification is because with binary -- its either yes or no. So 1 binary column can record that. If you just remove a random column for one of your 3 shapes -- say 'square' -- then haven't you just lost that information from your dataset? I guess you could infer that since there are only 3 discrete categories -- a '0' value for circle/oval implies that it must be a square. But then how would the presence of 'square' be returned as a predictive value in a later model, if square isn't an explicitly listed option? In the case with 2 separate "Pink" and "Yellow" values -- both would be exactly correlated with one another, as the dichotomy is either/or. They are perfect opposites, and the absence of 1 of the 2 options enables you to infer the value 100% of the time. In the case of 3 variables -- each of these columns would not represent a similar symmetric/binary relationship- as the absence of "square" doesn't allow you to directly infer the presence of either circle/oval as an alternative, as the absence of Pink enables you to do for Yellow. Having 2 alternatives instead of 1 introduces ambiguity that is not present in a binary relationship Anyways just my thought. Thank you for the great content!

YOU ARE AWESOME!

Well my understanding says that "a binary feature when one-encoded will always give a 2*2 Matrix and non-binary is always n*2 Matrix". This could be the supporting pillar for using "if_binary" as it removes redundancy from a very near Identity Matrix.