Greatest accuracy in the |mn> state is |n| = m

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How do we show that the greatest accuracy in the |mn> state is |n| = m for the Mx and My components?
 

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Yes M is an angular momentum operator. I also know that the components Mx and My do not commute. However, I do not understand how to show the greatest accuracy.

Are you saying that Mx and My are orthogonal since they do not commute?
 

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