Question Bank MCQ • 2 Marks Section 1: Mathematical Physics Mathematical Physics - Module 4

QB_PH_010: Mathematical Physics - Module 4

Question Statement

A $3 \times 3$ matrix $M$ has eigenvalues $1$, $2$, and $-3$. The determinant of $M^3 - 2M + I$ is:
(A) 0
(B) -100
(C) 120
(D) -200
Correct Answer
A
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: For eigenvalue $\lambda = 1$, $\mu = 1^3 - 2(1) + 1 = 0$. Since an eigenvalue is 0, $\det = 0$.
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