Answer
The determinant of the given matrix is zero therefore it has no inverse.
Refer to the step-by-step part for the solution.
Work Step by Step
We know that for a matrix
\[
\left[\begin{array}{rrr}
a & b & c \\
d &e & f \\
g &h & i \\
\end{array} \right]
\]
the determinant, $D=a(ei-fh)-b(di-fg)+c(dh-eg).$
We also know that if $D=0$, the matrix has no inverse.
Hence here $D=(-3)((-4)\cdot5-(-7)\cdot2)-1(1\cdot5-(-7)\cdot1)+(-1)(1\cdot2-(-4)\cdot1)=(-3)(-6)-(1)(12)+(-1)(6)=18-12-6=0.$
The determinant is zero therefore the given matrix has no inverse.
