Which of the following is NOT correct?

The correct answer is Option (4) → If a square matrix is invertible, then it may have more than one inverse.

Each option is checked as a statement; the answer is the statement that is false.

Option (1) If matrix B is the inverse of matrix A, then A is the inverse of B. — Correct. AB = BA = I says both that B is the inverse of A and that A is the inverse of B.

Option (2) A rectangular matrix of order \(m \times n, m \ne n\) does not possess an inverse. — Correct. AB = BA = I needs both products to be defined and of the same order, which happens only for square matrices.

Option (3) If A and B are symmetric matrices of the same order, then (AB-BA) is a skew-symmetric matrix. — Correct. Using \((AB)^T = B^TA^T\) and \(A^T = A,\ B^T = B\):

    \((AB - BA)^T = B^TA^T - A^TB^T = BA - AB = -(AB - BA)\)

Option (4) If a square matrix is invertible, then it may have more than one inverse. — Incorrect. The inverse is unique. If B and C are both inverses of A, then

    \(B = BI = B(AC) = (BA)C = IC = C\)

NCERT (2026-27 edition):
Invertible Matrices