Answer
False
Work Step by Step
If $A$ is an $n \times n$ matrix with $\det(A) = 0$, $A$ can not be invertible. Hence, columns of $A$ don't form a basis for $R^n$. Hence, the statement is false.
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 4 - Vector Spaces - 4.10 Invertible Matrix Theorem II - True-False Review - Page 332: d
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