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 $D=1((-4)\cdot1-1\cdot7)-1(2\cdot1-1\cdot(-5))+(-3)(2\cdot7-(-4)\cdot(-5))=(1)(-11)-(1)(7)+(-3)(-6)=-11-7+18=0.$
The determinant is zero therefore the given matrix has no inverse.
