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GATE DS&AI 2024 | Question: 25
Arjun
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Consider the $3 \times 3$ matrix $\boldsymbol{M}=\left[\begin{array}{lll}1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6\end{array}\right]$.
The determinant of $\left(\boldsymbol{M}^{2}+12 \boldsymbol{M}\right)$ is $\_\_\_\_\_\_\_\_\_$.
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Since row transformation $R_3 \leftarrow R_3-(R_1+R_2)$ makes $\det(M)=0$
Hence, $\det(M^2+12M)=\det(M(M+12I))=\det(M)\det(M+12I)=0$
$\because \det(AB)=\det(A)\det(B)$ where A and B are square matrices of the same order.
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determinant is 0
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