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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
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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