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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If $A =\left[\begin{array}{ll}0 & 1 \\ 1 & 2\end{array}\right]$, then adj A will be :
  • ✓
    $\left[\begin{array}{cc}2 & -1 \\ -1 & 0\end{array}\right]$
  • B
    $\left[\begin{array}{cc}2 & -1 \\ -2 & 0\end{array}\right]$
  • C
    $\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\right]$
  • D
    $\left[\begin{array}{cc}-2 & -1 \\ -1 & 0\end{array}\right]$
✓

Answer

Correct option: A.
$\left[\begin{array}{cc}2 & -1 \\ -1 & 0\end{array}\right]$
(A)
$A _{11}=2, A_{12}=-1, A_{21}=-1, A_{22}=0$$
\operatorname{adj} A=\left[\begin{array}{ll}
A_{11} & A_{12} \\
A_{21} & A_{22}
\end{array}\right]^{\prime}=\left[\begin{array}{cc}
2 & -1 \\
-1 & 0
\end{array}\right]^{\prime}=\left[\begin{array}{cc}
2 & -1 \\
-1 & 0
\end{array}\right]
$
Hence correct option is (A).

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