ax + y + 1=0, x + y + a = 0 এবং x + ay +1 = 0 রেখা তিনটি সমবিন্দু হলে, a এর মান হবে-

রেখাত্রয় সমবিন্দু হলে $\left|\begin{array}{lll}\mathrm{a} & 1 & 1 \\ 1 & 1 & \mathrm{a} \\ 1 & \mathrm{a} & 1\end{array}\right|=0 \Rightarrow\left|\begin{array}{ccc}\mathrm{a}-1 & 0 & 1 \\ 0 & 1-\mathrm{a} & \mathrm{a} \\ 1-\mathrm{a} & \mathrm{a}-1 & 1\end{array}\right|=0\left[\mathrm{C}_{1}^{\prime}=\mathrm{C}_{1}-\mathrm{C}_{2}, \mathrm{C}_{2}^{\prime}=\mathrm{C}_{2}-\mathrm{C}_{3}\right]$

$\begin{array}{l} \Rightarrow(a-1)^{2}\left|\begin{array}{ccc} 1 & 0 & 1 \\ 0 & -1 & a \\ -1 & 1 & 1 \end{array}\right|=0\left[C_{1}^{\prime}=\frac{C_{1}}{(a-1)}, C_{2}^{\prime}=\frac{C_{2}}{(a-1)}\right] \\ \Rightarrow(a-1)^{2}[1(-1-a)-0+1(0-1)]=0\left[r_{1}\right. \text { বরাবর বিস্তার] } \\ \Rightarrow(a-1)^{2}[-1-a-0-1]=0 \Rightarrow(a=1)^{2}(-a-2)=0 \\ \therefore a-1=0 \Rightarrow a-1 ;-a-2=0 \Rightarrow a=-2 \therefore a=1,-2 \end{array}$