Let $$A = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{bmatrix}$$ and $$B = \begin{bmatrix} 3 & 4 & 1 & 2 \\ 4 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 \end{bmatrix}.$$ 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?

Let A = bmatrix 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 bmatrix and B = bmatrix 3 & 4 & 1 & 2 \\ 4 & 1 & 2 & 3 \\ 1 & 2 & 3 & 4 \\ 2 & 3 & 4 & 1 bmatrix. Let (A) and (B) denote the determinants of the matrices A and B, respectively. Which one of the options given below is TRUE?

Topic-wise GATE CS PYQs with verified steps