The value of $\lambda $ for which the matrix product $\begin{bmatrix} 2 & 0 & 7\\0 & 1& 0\\1 & -2 & 1\end{bmatrix} \begin{bmatrix} -\lambda & 14 \lambda & 7 \lambda \\0 & 1 & 6\\ \lambda & -4\lambda & -2\lambda \end{bmatrix}$ is an identity matrix is :

$\frac{1}{5}$

The correct answer is Option (4) → $\frac{1}{5}$

$\begin{bmatrix} 2 & 0 & 7\\0 & 1& 0\\1 & -2 & 1\end{bmatrix} \begin{bmatrix} -\lambda & 14 \lambda & 7 \lambda \\0 & 1 & 6\\ \lambda & -4\lambda & -2\lambda \end{bmatrix}=\begin{bmatrix} 1 & 0 & 0\\0 & 1& 0\\0 & 0 & 1\end{bmatrix}$

$⇒-2λ+7λ=1$

$⇒5λ=1$

$⇒λ=\frac{1}{5}$