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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Matrices

NDA 2021 · Mathematics · Matrices

Consider the following in respect of the Matrix A=[ array lll 1 & 1...

Consider the following in respect of the Matrix A=\left[111111111\begin{array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right] 1. Inverse of Adoesnotexist2.does not exist 2.A^3=A3.3A=A23. 3 A=A^2 Which of the above are correct?

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1, 2 and 3

Correct answer

C. 1 and 3 only

Step-by-step solution

∣A∣=0|A|=0, So inverse of A does not exist. A2=∣111111111∣×∣111111111∣=∣333333333∣=3A∴A3=9A.\begin{aligned} & A^2=\left|\begin{array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right| \times\left|\begin{array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right|=\left|\begin{array}{lll} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \end{array}\right|=3 A \\ & \therefore A^3=9 A . \end{aligned}
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