For the system of equations AX = B, which of the following is correct?

The correct answer is Option (3) → If A is a non-singular matrix, then AX = B has a unique solution.

If A is non-singular (\(|A| \ne 0\)), then \(A^{-1}\) exists and

    \(X = A^{-1}B\)

is the one and only solution.

If A is singular (\(|A| = 0\)), the system never has a unique solution: it has either no solution (inconsistent) or infinitely many solutions.

So only Option (3) is true; Options (1) and (4) fail for singular A, and Option (2) contradicts the unique solution \(X = A^{-1}B\).

NCERT (2026-27 edition):
Solution of System of Linear Equations Using Inverse of a Matrix