GATE CS 1997 Q1.3 — Linear Algebra: Matrices, Determinants, System of Linear Equations

The given matrix is an upper triangular matrix because all elements below the main diagonal are zero:

For any upper triangular (or lower triangular) matrix, the determinant is simply the product of its diagonal elements.

The diagonal elements of the matrix $A$ are $6$, $2$, $4$, and $-1$.

Therefore, the correct option is B.