Does swapping rows change the determinant?

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Solution

Interchange the column or row of Matrices:
Yes, by swapping the rows, the determinant will be changed.
Let, $A = (\begin{matrix} 1 & - 2 \\ 5 & 1 \end{matrix})$ is a matrix.
Therefore, $d e t (A) = (1 + 10) = 11$
If we change the rows, then the new matrix will be $A' = (\begin{matrix} 5 & 1 \\ 1 & - 2 \end{matrix})$ .
Here, $d e t (A) = (- 10 - 1) = - 11$
Therefore, swapping the rows change the determinant value.

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Similar questions

Q. Which of these are correct?

(a)

If any two rows or columns of a determinant are identical, then the value of the determinant is zero.

(b)

If the corresponding rows and columns of a determinant are interchanged, then the value of the determinant does not change.

(c)

If any two rows (or column) of a determinant are interchanged, then the value of the determinant changes in sign.

Verify property $2$ for
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} 2 & - 3 & 5 6 & 0 & 4 1 & 5 & - 7 \end{matrix} ∣ ∣ ∣ ∣$
Property $2 :$ If any two rows (or columns) of a determinant are interchanged, then sign of determinant changes.

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Q. Assertion :The determinant of

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 5 & 6 & 7 2 & 4 & 6 \end{matrix} ⎤ ⎥ ⎦

is zero Reason: The determinant of a matrix vanishes if any two rows or columns are proportional.

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Does swapping rows change the determinant?

Interchange the column or row of Matrices:Yes, by swapping the rows, the determinant will be changed.Let, A=1-251 is a matrix.Therefore, det(A)=(1+10)=11If we change the rows, then the new matrix will be A'=511-2.Here, det(A)=(-10-1)=-11Therefore, swapping the rows change the determinant value.