Q58 / 160 · AP EAMCET 2009 · Mathematics

If $\left[\begin{array}{rrr}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse, then the real value of $x$ is

  • A
    2
  • B
    3
  • C
    0
  • Correct answer
    D
    1

Solution

If matrix has no inverse it means the value of determinant should be zero. $\therefore \quad\left|\begin{array}{rrr} 1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1 \end{array}\right|=0$ If we put $x=1$, then column Ist and IIIrd are identical. Hence, option (d) is correct.

Hence, the correct answer is option: 'D'.

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