Good day to all,

While reading my professor's notes on matrix inverses he asks if we can tell without computing why the following equation (attached image) is not true

with the X meaning multiplication.

I feel embarrassed asking the question but I cannot seem to see why. At first I thought it was because the maximum rank of the first matrix is 3 as well as the second's while the resulting matrix rank is 4. But I am not sure if this is the avenue I should be exploring. What I am seeking is some guidance and not necessarily the answer. Any help would be greatly appreciated.

Kindest regards