Gate CS 2023 | Question - 18 | Engineering Mathematics

Let

$A = [\begin{matrix} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{matrix}]$

and

$B = [\begin{matrix} 3 & 4 & 1 & 2 \\ 4 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 \end{matrix}]$

Let det(A) and det(B) denote the determinants of the matrices A and B, respectively.

Which one of the options given below is TRUE?

det(A) = det(B)

det(B) = −det(A)

det(A) = 0

det(AB) = det(A) + det(B)

Solution:

If we interchange the R1 ⇔ R2 of A, then Matix A become Matrix B

According to the property of any determinant if two rows (or 2 columns) of a determinant are interchanged the sign of the value of the determinant is changed.

Here only one-time rows are changed so the determinant should be multiplied by (−1).

So, the Option B is correct.

det(B) = −det(A)

Gate CS 2023 | Question - 18 | Engineering Mathematics

Related Topics