Question

The determinant of the matrix \[ \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{pmatrix} \] is equal to

• A. -1
• B. 0
• C. 1
• D. None of these

Hint:

When the rows or columns of a matrix are linearly dependent, the determinant will be 0. This is the case with the provided matrix.

Answer 1

The Correct Option is B

The determinant of the given matrix is computed as follows: \[ \text{Determinant} = 1 \times \begin{vmatrix} 5 & 6 \\ 8 & 9 \end{vmatrix} - 2 \times \begin{vmatrix} 4 & 6 \\ 7 & 9 \end{vmatrix} + 3 \times \begin{vmatrix} 4 & 5 \\ 7 & 8 \end{vmatrix} \] Upon calculation, we find that the determinant is 0.