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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If cofactor $C _{i j}$ represent for element $p_{i j}$, of matrix $P =\left[\begin{array}{ccc}1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & 2 & 4\end{array}\right]$ then value of $C_{31} . C_{23}$ is :
  • ✓
    5
  • B
    24
  • C
    -24
  • D
    -5
✓

Answer

Correct option: A.
5
(A)
$
\begin{array}{l}
C_{31}=(-1)^{3+1}\left|\begin{array}{cc}
-1 & 2 \\
2 & -3
\end{array}\right|=3-4=-1 \\
C_{23}=(-1)^{2+3}\left|\begin{array}{cc}
1 & -1 \\
3 & 2
\end{array}\right|=-(2+3)=-5
\end{array}
$
Hence $C_{31} \cdot C_{23}=(-1)(-5)=5$

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