TS EAMCET 2017 Code A Solved Paper

Consider the given matrix $A=\begin{pmatrix} x & x & x \\ x & x^{2} & x \\ x & x & x+1 \end{pmatrix}$ since rank of the matrix is $1,$ therefore, it should have at leastone non-zero determinant of order 1 and all the higher orderdeterminants should be zero. If $x=0$ $A=\begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 1 \end{pmatrix}$ It has non zero determinant of order 1 only. If $x=1$ $A=\begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 2 \end{pmatrix}$ It has a non zero determinant of order $2,$ nearly $\begin{vmatrix} 1 & 1 \\ 1 & 2 \end{vmatrix}$ Therefore, x can take value 0 only.