GATE 2024 DA – Question 35
Consider the $3 \times 3$ matrix $\boldsymbol{M} = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix}$.
The determinant of $(\boldsymbol{M}^2 + 12\boldsymbol{M})$ is ______.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 0
Explanation
Since $M^2 + 12M = M(M + 12I)$, its determinant is $\det(M)\det(M + 12I)$. The determinant of $M$ is $1(6 - 9) - 2(18 - 12) + 3(9 - 4) = -3 - 12 + 15 = 0$, so the product is 0.