If A and B are invertible matrices of the same order, then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \((AB)^{-1}=B^{-1}A^{-1}\)
By the reversal law for inverses, the inverse of a product is the product of the inverses in the reverse order. Check:
\((AB)(B^{-1}A^{-1}) = A(BB^{-1})A^{-1}\)
\(= AIA^{-1} = AA^{-1} = I\)
In the same way \((B^{-1}A^{-1})(AB) = I\), so \((AB)^{-1} = B^{-1}A^{-1}\).
Why the other options are incorrect
Option (1) \(AB = BA\) — Incorrect. Matrix multiplication is not commutative, even for invertible matrices.
Option (3) \((AB)^{-1}=A^{-1}B^{-1}\) — Incorrect. The order is not reversed; \(A^{-1}B^{-1}\) equals \((BA)^{-1}\), not \((AB)^{-1}\).
Option (4) \(AB^{-1}=B^{-1}A\) — Incorrect. This would need A and \(B^{-1}\) to commute, which is not true in general.
NCERT (2026-27 edition):
Invertible Matrices
