The value of x for which the matrix product $\begin{bmatrix}2&0&7\\0&1&0\\1&-2&1\end{bmatrix}\begin{bmatrix}-x &14x&7x\\0&1&0\\x&- 4x& -2x\end{bmatrix}$ equals an identity matrix, is

1/5

We have,

$\begin{bmatrix}2&0&7\\0&1&0\\1&-2&1\end{bmatrix}\begin{bmatrix}-x &14x&7x\\0&1&0\\x&- 4x& -2x\end{bmatrix}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$

$⇒\begin{bmatrix}5x&0&0\\0&1&0\\0&10x-2&2x\end{bmatrix}=\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$

$⇒5x=1, 10x-2=0⇒ x=\frac{1}{5}$