The system of linear equations \[ \begin{array}{l} x+y+z=2 \\ 2 x+3...

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The system of linear equations
\[
\begin{array}{l}
x+y+z=2 \\
2 x+3 y+2 z=5 \\
2 x+3 y+\left(a^{2}-1\right) z=a+1
\end{array}
\]
\( \mathrm{P} \)
(1) is inconsistent when \( a=4 \)
(2) has infinitely many solutions for \( a=4 \)
(3) is inconsistent when \( |a|=\sqrt{3} \)
(4) has a unique solution for \( |a|=\sqrt{3} \)
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