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NDA 2017 Maths · Mathematics · Matrices · hard

How many 2×2 matrices with every entry equal to 0 or 1 are singular?

Single correct option

How many 2×22\times2 matrices with every entry equal to 0 or 1 are singular?
  1. A. 66
  2. B. 1010
  3. C. 88
  4. D. 1212
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Answer: (B) 1010

There are 24=162^4=16 matrices. The determinant ad−bcad-bc is non-zero only when exactly one of ad,bcad,bc equals 1: ad=1,bc=0ad=1,bc=0 gives 3 ways and bc=1,ad=0bc=1,ad=0 gives 3 ways, i.e. 6 non-singular matrices. Singular ones are 16−6=1016-6=10.
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Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake