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GATE DA 2024 Set 1 — Question 35

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NAT+1 / -0MediumDeterminant CalculationLU Decomposition & DeterminantsLinear AlgebraDeterminant PropertiesMatrix Multiplication & ConformabilityMatrix Algebra

Linear Algebra → LU Decomposition & Determinants → Determinant Calculation

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Question

Consider the 3×33 \times 3 matrix M=[123313436]M = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 3 \\ 4 & 3 & 6 \end{bmatrix}.
The determinant of (M2+12M)(M^2 + 12M) is ______.
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