Which of the following matrices is singular?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\begin{bmatrix}3 & -2\\ 6 & -4\end{bmatrix}\)
A square matrix is singular when its determinant is 0.
\( 3 \times (-4) - (-2) \times 6 = -12 + 12 = 0 \)
Its second row (6, −4) is twice the first row (3, −2), which is why the determinant vanishes.
Why the other options are incorrect
Option (1) \(\begin{bmatrix}2 & 5\\ 1 & 3\end{bmatrix}\) — Incorrect. Determinant \(6 - 5 = 1 \ne 0\).
Option (2) \(\begin{bmatrix}4 & -2\\ 3 & 1\end{bmatrix}\) — Incorrect. Determinant \(4 + 6 = 10 \ne 0\).
Option (3) \(\begin{bmatrix}-3 & 2\\ 6 & 4\end{bmatrix}\) — Incorrect. Determinant \(-12 - 12 = -24 \ne 0\).