Question

Let |A|=k.If B is the matrix obtained by interchangeing two rows of A then |B|=?​

Answer 1

Answer:

1B1=k. There is no change by interchange of two rows.

Answer 2

Given:

$\mid A\mid=k$

B is the matrix obtained by interchanging two rows of A

To find:

$\mid B\mid$

Solution:

$\mid A\mid =k$

Matrix B is obtained by interchanging the two rows of A

We know that

When the rows or columns of a matrix interchanged then the value of determinant does not change.

Therefore, by using this property

$\mid B\mid =\mid A\mid$

$\mid B\mid=k$

Hence,$\mid B\mid=k$