If A = [ * 20 c &0 1&1 ] and B = [ * 20 c 1&0 5&1 ], then value o… - Vidyadip

MCQ

If $A = \left[ {\begin{array}{*{20}{c}}\alpha &0\\1&1\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}1&0\\5&1\end{array}} \right]$, then value of $\alpha $for which ${A^2} = B$, is

A
$1$
B
$-1$
C
$4$
✓
No real values

✓

Answer

Correct option: D.

No real values

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

Clearly, no real value of $\alpha$.

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