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GATE BT 2026 | Question: 31

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For the given matrix, which of the statements given below is/are true?

\[
\left[\begin{array}{ccc}
3 & 1 & 5 \\
2 & -1 & 0 \\
5 & 2 & 9
\end{array}\right]
\]

  1. The matrix is full rank
  2. The matrix is invertible
  3. The matrix has a determinant
  4. The matrix has a transpose

1 Answer

1 1 vote

C. The matrix has a determinant: True. Every square matrix has a determinant (in this case, it equals 0).

D. The matrix has a transpose: True. Every matrix always has a transpose.

The other two are false because the determinant is |0| (making it not full rank and not invertible)

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