If $A=\left[\begin{array}{cc}\mathrm{k} & 2 \ -2 & -\mathrm{k}\end{array} ight]$, then $\mathrm{A}^{-1}$ does not exists if $\mathrm{k}=$

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If $A=\left[\begin{array}{cc}\mathrm{k} & 2 \ -2 & -\mathrm{k}\end{array}ight]$, then $\mathrm{A}^{-1}$ does not exists if $\mathrm{k}=$

Aicharya · Accepted Answer

$\begin{aligned} & A=\left[\begin{array}{cc} \mathrm{k} & 2 \ -2 & -\mathrm{k} \end{array}ight] \ & 	herefore|\mathrm{A}|=\left[\begin{array}{cc} \mathrm{k} & 2 \ -2 & -\mathrm{k} \end{array}ight]=-\mathrm{k}^2+4 \end{aligned}$ When $-\mathrm{k}^2+4=0$, we get $\mathrm{k}= \pm 2$

If $A=\left[\begin{array}{cc}\mathrm{k} & 2 \\ -2 & -\mathrm{k}\end{array}\right]$, then $\mathrm{A}^{-1}$…

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