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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Matrices

NDA 2017 · Mathematics · Matrices

Consider the set A of all matrices of order 3 × 3 with entries 0 or...

Consider the set A of all matrices of order 3×33 \times 3 with entries 0 or 1 only. Let BB be the subset of AA consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is -1. Then which one of the following is correct?

Options

  1. AC is empty
  2. BB has as many elements as C
  3. CA=B∪C\mathrm{A}=\mathrm{B} \cup \mathrm{C}
  4. DB has thrice as many elements as C

Correct answer

B. B has as many elements as C

Step-by-step solution

determinant of B=1\mathrm{B}=1 Let ' BB ' be identity matrix So, B=\left|100010001\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right| If we interchange any 2 rows, determinant will be -1 Let, \mathrm{C}=\left|100001010\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right|,|\mathrm{C}|=-1 Here, number of elements in B and C are equal.
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