The solution X of the matrix equation AX = B, where A is an invertible matrix, is given by
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(X=A^{-1}B\)
Since A is invertible, multiply both sides of AX = B by \(A^{-1}\) on the left:
\(A^{-1}(AX) = A^{-1}B\)
\(\left(A^{-1}A\right)X = A^{-1}B\)
\(IX = A^{-1}B\)
\(X = A^{-1}B\)
Why the other options are incorrect
Option (1) \(X=BA^{-1}\) — Incorrect. Here \(A^{-1}\) is on the wrong side; since matrix multiplication is not commutative, \(BA^{-1} \ne A^{-1}B\) in general.
Option (3) \(X=A^{-1}B^{-1}\) — Incorrect. B is not inverted; B need not even be invertible.
Option (4) \(X=AB^{-1}\) — Incorrect. Then \(AX = A^2B^{-1}\), which is not B in general.
NCERT (2026-27 edition):
Solution of System of Linear Equations Using Inverse of a Matrix
