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Question: Answered & Verified by Expert
If $A=\left[\begin{array}{ccc}1 & -2 & -3 \\ 2 & 1 & -2 \\ 3 & 2 & 1\end{array}\right]$, then which one of the following is
correct?
MathematicsMatricesNDANDA 2009 (Phase 2)
Options:
  • A $A$ is symmetric matrix
  • B $A$ is anti- symmetric matrix
  • C $A$ is singular matrix
  • D $A$ is non-singular matrix
Solution:
1780 Upvotes Verified Answer
The correct answer is: $A$ is non-singular matrix
Here we see that its diagonal elements are not zero, so it is not anti-symmetric matrix. Now, $|\mathrm{A}|=1(1+4)+2(2+6)-3(4-3)$
$=5+16-3=18 \neq 0$
Hence, it is non-singular matrix.

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