Answer
True
Work Step by Step
If $A$ and $B$ are invertible $n \times n$ matrices, we can express it as:
$(AB)B^{-1}A^{-1}=I_n\\
B^{-1}A^{-1}(AB)=I_n$
We can see $AB$ having an inverse $B^{-1}A^{-1}$ is invertible.
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 2 - Matrices and Systems of Linear Equations - 2.6 The Inverse of a Square Matrix - True-False Review - Page 177: f
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