Allied & ICAR Exam Bank • ALLIED_0009 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

If $\lambda$ is an eigenvalue of an invertible matrix $A$, then an eigenvalue of $A^{-1}$ is:

Options:

  • (A) $1/\lambda$
  • (B) $\lambda$
  • (C) $-\lambda$
  • (D) $\lambda^2$

Answer Key:

A

Step-by-Step Solution & Explanation

If $A v = \lambda v$, then multiplying by $A^{-1}$ gives $v = \lambda A^{-1} v \implies A^{-1} v = (1/\lambda) v$.
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