Which of the following matrices is singular?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\begin{bmatrix}2 & 3\\ 4 & 6\end{bmatrix}\)
A matrix is singular when its determinant is zero.
\(2 \cdot 6 - 3 \cdot 4 = 12 - 12 = 0\)
The second row is twice the first row, which is why the determinant is zero.
Why the other options are incorrect
Option (1) \(\begin{bmatrix}1 & 2\\ 3 & 4\end{bmatrix}\) — Incorrect. Its determinant is 4 − 6 = −2, not zero.
Option (3) \(\begin{bmatrix}3 & -1\\ 6 & 2\end{bmatrix}\) — Incorrect. Its determinant is 6 + 6 = 12, not zero.
Option (4) \(\begin{bmatrix}5 & 2\\ 2 & 1\end{bmatrix}\) — Incorrect. Its determinant is 5 − 4 = 1, not zero.