Method 1: Check if its rank is 1. If it is 1, it can be written as a row (a) multiplied by a column (b), that is, A=ab. In this case, A^2=a(ba)b. Note that ba is a number here, so we can conclude that A^2=(ba)A;

Method 2: See if it can be diagonalized. If it can, there exists a reversible matrix a, such that a^(-1)Aa=∧, so A=a∧a^(-1), A^2=a∧a^(-1)a∧a^(-1)=a∧^2a^(-1); finally, use the most primitive method of multiplication, matrix multiplication.