Method 1: To see if its rank is 1, if it is 1, it must be written as a row (a) multiplied by a column (b), that is, A=ab. In this case, A^2=a(ba)b, and notice that ba is A number here, we can argue that A^2=(ba)A;

Method 2: See if he can diagonalize, if there is an inverse matrices a, such that a^(-1)Aa=∧, So A=a∧a^(-1), A^2=a∧a^(-1), a∧a^(-1)=a∧^2a^(-1); Finally, multiply by the original method and matrices subtraction.