If $\begin{bmatrix}a_1 & b_1 & c_1\\a_2 & b_2 & c_2\\a_3 & b_3 & c_3\end{bmatrix}=5, $ then the value of $Δ=\begin{bmatrix}b_2c_3-b_3c_2 & a_3c_2-a_2c_3 &a_2b_3-a_3b_2\\b_3c_1-b_1c_3 & a_1c_3-a_3c_1 & a_3b_1-a_1b_3\\b_1c_2-b_2c_1 & a_2c_1-a_1c_2 & a_1b_2-a_2b_1\end{bmatrix}$, is
Answer & explanation
Correct answer: option 2
The correct answer is option (2) : 125
We know that if A' is a square matrix of order n and B is the matrix of cofactors of element s of A. Then,
$|B|=A|^{n-1}$
Here, Δ is the determinant of cofactors of elements of matrix A given by
$A=\begin{bmatrix}a_1 & b_1 & c_2\\a_2 & b_2 & c_2\\a_3 & b_3 & c_3\end{bmatrix}$
$∴Δ=|A|^{3-1}=|A|^2=5^2= 25 $