Answer
True
Work Step by Step
We have $e^{At}=I_{n \times n}+At+\frac{(At)^2}{2!}+\frac{(At)^3}{3!}+...$
To satisfy all the condition above, $A$ should be a square matrix.
Hence, the statement is true.
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 7 - Eigenvalues and Eigenvectors - 7.4 An Introduction to the Matrix Exponential Function - True-False Review - Page 465: a
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