Chapter 2 - Matrices and Systems of Linear Equations - 2.6 The Inverse of a Square Matrix - True-False Review - Page 177: g

True

If $A$ is an invertible $n \times n$ matrices, such that $A^2=A\\ \rightarrow A^2-A=0\\ \rightarrow A(A-I)=0$ Multiplying both sides by $A^{-1}$ $\rightarrow A^{-1}A(A-I)=A^{-1}0\\ \rightarrow A-I=0\\ \rightarrow A=I$ Hence, $A$ is the identify matrix. Hence, the statement is true