Question

If $\left|\begin{array}{ccc}1& -1& x\\ 1& x& 1\\ x& -1& 1\end{array}\right|$ has no inverse, then the real value of $x$ can be is

• A. 2
• B. 3
• C. 0
• D. 1

Answer 1

The correct option is D 1

$\left|\begin{array}{ccc}1& -1& x\\ 1& x& 1\\ x& -1& 1\end{array}\right|$

No inverse

$\Rightarrow \left|A\right|=0$

$x+1+1(1-x)+x(-1-x^2)=0$

$x+1+1-x-x-x^3=0$

$x^3-x-2=0$

$\Rightarrow x^3+2x-x-2=0$

$(x^2-1)(x+2)=0$

$\Rightarrow x=\pm 1,x=-2$

Real value of $x=1$

Option D