Find X , using the inverse of matrices Find the value of $X$ if
$$\begin{pmatrix}2&  0& 7\\ 0 & 1& 0 \\ 1& -2& 1 \\ \end{pmatrix} \begin{pmatrix}-X&  14X& 7X\\ 0 & 1& 6 \\ X& -4X& -2X \\  \end{pmatrix} = \begin{pmatrix}1&  0& 0\\ 0 & 1& 0 \\ 0& 0& 1 \\  \end{pmatrix}$$
I tried to solve the question by finding the inverse of the matrix on the left side, then multiplying both sides by that inverse matrix to be able to solve for X.
I got X=1/5, but the problem is I got 6 = 0 which means inconsistent system.
Please help!!

Let $A=\begin{pmatrix}
2 & 0 & 7 \\
0 & 1 & 0 \\
1 & -2 & 1
\end{pmatrix}$, note that det(A)=-5, so A is nonsingular.
Since $AA^{-1}=I$, according to the equation, you have: $A^{-1}=\begin{pmatrix}
-X & 14X & 7X \\
0 & 1 & 6 \\
X & -4X & -2X
\end{pmatrix}$
After computation, $A^{-1}= \begin{pmatrix}
 -0.2 & 2.8 & 1.4\\
    0 & 1 & 0 \\
  0.2 & -0.8 & -0.4
\end{pmatrix}$
$\underline{Edit}$: Notice that $6\neq 0$, referring to $A^{-1}_{(2,3)}$, so there is no solution for X.
