For the system of linear equations $a x+y+z=1$, $x+a y+z=1, x+y+a z=\beta$, which one of the following statements is NOT correct ?
For the system of linear equations $a x+y+z=1$, $x+a y+z=1, x+y+a z=\beta$, which one of the following statements is NOT correct ?
- [JEE MAIN 2023]
- A
It has infinitely many solutions if $\alpha=2$ and $\beta=-1$
- B
It has no solution if $\alpha=-2$ and $\beta=1$
- C
$x+y+z=\frac{3}{4}$ if $\alpha=2$ and $\beta=1$
- D
It has infinitely many solutions if $\alpha=1$ and $\beta=1$
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{{c_1}}&{{c_2}}&{{c_3}}
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{{a_1}}&{{a_2}}&{{a_3}} \\
{{b_1}}&{{b_2}}&{{b_3}} \\
{{c_1}}&{{c_2}}&{{c_3}}
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