If A = [ * 20 c &1 - 1 & - ], then for what value of , , A^2 = O - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}\lambda &1\\{ - 1}&{ - \lambda }\end{array}} \right]$, then for what value of $\lambda ,\,{A^2} = O$

A
$0$
✓
$ \pm {\rm{ }}1$
C
$-1$
D
$1$

✓

Answer

Correct option: B.

$ \pm {\rm{ }}1$

b
(b) ${A^2} = A\,.\,A = \left[ {\begin{array}{*{20}{c}}\lambda &1\\{ - 1}&{ - \lambda }\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}\lambda &1\\{ - 1}&{ - \lambda }\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{{\lambda ^2} - 1}&0\\0&{ - 1 + {\lambda ^2}}\end{array}} \right] = 0$

(As given)

==> ${\lambda ^2} - 1 = 0 \Rightarrow \lambda = \pm 1$.

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