If ka kb kckd ke kfkg kh ki-A anda b cd e fg h i-BThen the value of A-B is

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Properties of Determinants

If ka kb ...

Question

$If ∣ ∣ ∣ ∣ \begin{matrix} k a & k b & k c k d & k e & k f k g & k h & k i \end{matrix} ∣ ∣ ∣ ∣ = A and$
$∣ ∣ ∣ ∣ \begin{matrix} a & b & c d & e & f g & h & i \end{matrix} ∣ ∣ ∣ ∣ = B$
Then the value of $A / B$ is

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$k$

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$k^{3}$

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Solution

The correct option is C
$k^{3}$

It’s the property of the determinant that a scalar multiplied to a determinant will be same as the same scalar being multiplied to elements of one of the row or column of the same determinant. So if the scalar is multiplied to 3 rows or columns you can take out the scalar 3 times.
Given
$∣ ∣ ∣ ∣ \begin{matrix} k a & k b & k c k d & k e & k f k g & k h & k i \end{matrix} ∣ ∣ ∣ ∣ = A$

$\Rightarrow A = k^{3}$ $∣ ∣ ∣ ∣ \begin{matrix} a & b & c d & e & f g & h & i \end{matrix} ∣ ∣ ∣ ∣ = k^{3} B$

$∴ A / B = k^{3}$

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If ∣∣ ∣∣kakbkckdkekfkgkhki∣∣ ∣∣=A and ∣∣ ∣∣abcdefghi∣∣ ∣∣=B Then the value of A/B is

$If ∣ ∣ ∣ ∣ \begin{matrix} k a & k b & k c k d & k e & k f k g & k h & k i \end{matrix} ∣ ∣ ∣ ∣ = A and$
$∣ ∣ ∣ ∣ \begin{matrix} a & b & c d & e & f g & h & i \end{matrix} ∣ ∣ ∣ ∣ = B$
Then the value of $A / B$ is