Chapter 9 - Systems of Differential Equations - 9.8 Matrix Exponential Function and Systems of Differential Equations - True-False Review - Page 642: e

True

From equation 9.8.4, if A is an $n \times n$ matrix and $X(t)$ is any fundamental matrix for the corresponding vector differential equation $x′ = Ax$, then we can obtain: $$e^{At} = X(t)X^{-1}(0)$$ Hence, the statement is true.