GATE 2023 BM – Question 13
For $Q=\begin{pmatrix}1&-2\\2&1\end{pmatrix}$, which statement is true?
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Correct answer: (C) Q has full rank
Explanation
The determinant is 1×1−(−2)×2=5, which is nonzero. Thus both columns are independent and rank is two, the full rank of this matrix. The off-diagonal entries differ, so it is not symmetric; its inverse is one fifth of [[1,2],[−2,1]], not Q. Therefore C.