Allied & ICAR Exam Bank • ALLIED_1031 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrix inverse

Question Statement:

For any non-singular $n \times n$ matrix $A$ and non-zero scalar $c$, $(c A)^{-1}$ is equal to:

Options:

  • (A) \frac{1}{c} A^{-1}
  • (B) c A^{-1}
  • (C) \frac{1}{c^n} A^{-1}
  • (D) -c A^{-1}

Answer Key:

A

Step-by-Step Solution & Explanation

By property of matrix inverses, $(c A) \left(\frac{1}{c} A^{-1}\right) = \left(c \cdot \frac{1}{c}\right) (A A^{-1}) = 1 \cdot I = I$. Hence $(c A)^{-1} = \frac{1}{c} A^{-1}$.
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