Answer
The determinant for the given matrix is zero, so the matrix $A$ has no inverse.
Work Step by Step
The determinant for $3 \times 3$ matrix can be obtained as:
$det=\begin{vmatrix} a & b & c \\ d &e & f \\g &h & i \\
\end{vmatrix}=a(ei-fh)-b(di-fg)+c(dh-eg)$
Recall the determinant property that if $D=0$, then the matrix has no inverse.
We are given
$A=\begin{vmatrix} -3 & 1 & -1 \\ 1 &-4 & -7 \\1 &2 & 5 \\ \end{vmatrix}$
Now, $det A=(-3)((-4)5-(-7)2)-1(5-(-7)\cdot1)+(-1)(2-(-4))=(-3)(-6)-(1)(12)+(-1)(6)=18-12-6=0$
We can conclude that the determinant for the given matrix is zero and thus the matrix $A$ has no inverse.