If $A=\left[\begin{array}{cc}\lambda & i \ i & -\lambda\end{array} ight]$ and $A^{-1}$ does not exist, then $\lambda=($ where $I=\sqrt{-1})$

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If $A=\left[\begin{array}{cc}\lambda & i \ i & -\lambda\end{array}ight]$ and $A^{-1}$ does not exist, then $\lambda=($ where $I=\sqrt{-1})$

Aicharya · Accepted Answer

$A=\left[\begin{array}{cc} \lambda & \mathrm{i} \ \mathrm{i} & -\lambda \end{array}ight] \Rightarrow|\mathrm{A}|=\left|\begin{array}{cc} \lambda & \mathrm{i} \ \mathrm{i} & -\lambda \end{array}ight|$ Since $\mathrm{A}^{-1}$ does not exist, we write $|\mathrm{A}|=0$ $	herefore\left(-\lambda^2ight)-\left(\mathrm{i}^2ight)=0 \quad \Rightarrow \lambda^2=1 \Rightarrow \lambda= \pm 1$

If $A=\left[\begin{array}{cc}\lambda & i \\ i & -\lambda\end{array}\right]$ and $A^{-1}$ does not exist,…

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