Question

If A and B are n x n matrices, check the true statements below if two row interchanges are made in succession.

a. Determinant remains unchanged
b. Determinant becomes negative
c. Determinant doubles
d. Determinant halves

Answer 1

The determinant of a matrix becomes negative if two rows are interchanged in succession.

Step-by-step explanation:

The determinant of a matrix will change sign if two rows are interchanged. Therefore, the answer is b. Determinant becomes negative. Let's see an example:

Suppose we have the matrix A:

1 2

3 4

If we interchange the rows, we get the matrix B:

3 4

1 2

The determinant of A is 1*4 - 2*3 = -2, while the determinant of B is 3*2 - 4*1 = 2. So the determinant becomes negative when two row interchanges are made in succession.