The roots of the equation $\left| {\,\begin{array}{*{20}{c}}{x - 1}&1&1\\1&{x - 1}&1\\1&1&{x - 1}\end{array}\,} \right| = 0$  are

  • A

    $1, 2$

  • B

    $-1, 2$

  • C

    $1, -2$

  • D

    $-1, -2$

Similar Questions

The value of $'a'$ for which the system of equation  $a^3x + (a + 1)^3y + (a + 2)^3 z = 0$ ; $ax + (a + 1)y + (a + 2)z = 0$ ; $x + y + z = 0$  has a non-zero solution is :-

The existence of the unique solution of the system $x + y + z = \lambda ,$ $5x - y + \mu z = 10$, $2x + 3y - z = 6$ depends on

If $a, b, c$ are three complex numbers such that $a^2 + b^2 + c^2 = 0$ and  $\left| {\begin{array}{*{20}{c}}
{\left( {{b^2} + {c^2}} \right)}&{ab}&{ac}\\
{ab}&{\left( {{c^2} + {a^2}} \right)}&{bc}\\
{ac}&{bc}&{\left( {{a^2} + {b^2}} \right)}
\end{array}} \right| = K{a^2}{b^2}{c^2}$ then value of $K$ is

The system of equations  $-k x+3 y-14 z=25$  $-15 x+4 y-k z=3$  $-4 x+y+3 z=4$  is consistent for all $k$ in the set

  • [JEE MAIN 2022]

$\left| {\begin{array}{*{20}{c}}0&a&{ - b}\\{ - a}&0&c\\b&{ - c}&0\end{array}} \right| = $