Chapter 4 - Vector Spaces - 4.9 The Rank-Nullity Theorem - True-False Review - Page 330: e

True

Assume that $A$ is an invertible $n × n$ matrix and nullspace (A) = colspace (A) $A$ is invertible $\rightarrow nullspace (A)=0 \rightarrow colspace (A)=0$ Thus, $A$ is a null matrix. Since null matrix is non-invertible matrix, $A$ can not be an invertible matrix. Hence, the statement is true.