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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Matrices

NDA 2013 · Mathematics · Matrices

If A and B are two non-singular square matrices such that AB=A ,...

If AA and BB are two non-singular square matrices such that AB=A\mathrm{AB}=\mathrm{A}, then which one of the following is correct

Options

  1. ABB is an identity matrix
  2. BB=A−1\mathrm{B}=\mathrm{A}^{-1}
  3. CB=A2\mathrm{B}=\mathrm{A}^2
  4. DDeterminant of BB is zero

Correct answer

A. BB is an identity matrix

Step-by-step solution

A and B are 2 non singular matrix so A−1\mathrm{A}^{-1} and B−1\mathrm{B}^{-1} are defined A−1\mathrm{A}^{-1}\mathrm{AB}=\mathrm{A}−1A⇒B=I^{-1} \mathrm{ A} \quad \Rightarrow \mathrm{ B}=\mathrm{I}
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