If A = [ * 20 c x&1 1&0 ] and A^2 is the identity matrix, then x … - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}x&1\\1&0\end{array}} \right]$ and ${A^2}$ is the identity matrix, then $x =$

A
$1$
B
$2$
C
$3$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) $A = \left[ {\begin{array}{*{20}{c}}x&1\\1&0\end{array}} \right],\therefore {A^2} = I \Rightarrow \left[ {\begin{array}{*{20}{c}}x&1\\1&0\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}x&1\\1&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right]$

==> $\left[ {\begin{array}{*{20}{c}}{{x^2} + 1}&x\\x&1\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1&0\\0&1\end{array}} \right] \Rightarrow {x^2} + 1 = 1 \Rightarrow x = 0$.

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