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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Matrices

NDA 2018 · Mathematics · Matrices

If A and B are two invertible square matrices of same order, then...

If AA and BB are two invertible square matrices of same order, then what is (AB)−1(\mathrm{AB})^{-1} equal to?

Options

  1. AB−1A−1\mathrm{B}^{-1} \mathrm{ A}^{-1}
  2. BA−1B−1\mathrm{A}^{-1} \mathrm{ B}^{-1}
  3. CB−1A\mathrm{B}^{-1} \mathrm{ A}
  4. DA−1B\mathrm{A}^{-1} \mathrm{ B}

Correct answer

A. B−1A−1\mathrm{B}^{-1} \mathrm{ A}^{-1}

Step-by-step solution

(AB)−1=B−1A−1(\mathrm{AB})^{-1}=\mathrm{B}^{-1} \mathrm{ A}^{-1}
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