Answer
Yes an inverse exists, $det(A) = 4$
Work Step by Step
Let us extend the matrix and use Sarrus's rule.
$$
\begin{matrix}
2 & 1 & 0 &2 & 1 \\
0 & -2 & 4&0 & -2 \\
0 & 1 & -3 &0 & 1
\end{matrix}$$
$
2*-2*-3-8 = 4$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305115546
ISBN 13:
978-1-30511-554-5
Chapter 6, Matrices and Determinants - Section 6.4 - Determinants and Cramer's Rule - 6.4 Exercises - Page 534: 21
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