Answer
False.
Work Step by Step
False, a matrix is non-invertible if its determinant is $0$. Thus in case of a $2\times2$ matrix full of $1$s, its determinant is $0$ whereas it does not include a row of $0$s.
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 176: b
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