The number of all possible non-singular matrices of order \(2 \times 2\) with each entry 0 or 1 is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
Let the matrix be
\(A = \begin{bmatrix} a & b\\ c & d \end{bmatrix}, \quad a, b, c, d \in \{0, 1\}\)
A is non-singular when \(|A| = ad - bc \ne 0\). Each of ad and bc is 0 or 1, so \(|A| \ne 0\) only in two ways.
Case ad = 1, bc = 0: a = d = 1, and (b, c) is (0, 0), (0, 1) or (1, 0):
\(3 \text{ matrices}\)
Case ad = 0, bc = 1: b = c = 1, and (a, d) is (0, 0), (0, 1) or (1, 0):
\(3 \text{ matrices}\)
Total number of non-singular matrices:
\(3 + 3 = 6\)