Which of the following matrices is not invertible ?

The correct answer is Option (2) → \(\begin{bmatrix}2 & 3\\4 & 6\end{bmatrix}\)

A square matrix is invertible exactly when its determinant is not zero. For a 2 × 2 matrix the determinant is ad − bc.

    \(\text{Option (1)}: 1(1) - 1(0) = 1\)
    \(\text{Option (2)}: 2(6) - 3(4) = 12 - 12 = 0\)
    \(\text{Option (3)}: (-1)(5) - (-1)(-1) = -5 - 1 = -6\)
    \(\text{Option (4)}: 2(1) - (-2)(1) = 2 + 2 = 4\)

Only the matrix of Option (2) has determinant 0 (its second row is twice the first), so it is singular and not invertible.