Which of the following is NOT correct?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → If a square matrix is invertible, then it may have more than one inverse.
Check each statement.
If $B=A^{-1}$ then $A=B^{-1}$, so the first statement is correct.
A non-square matrix cannot have an inverse, so the second statement is correct.
If $A$ and $B$ are symmetric, then $(AB-BA)^{T}=B^{T}A^{T}-A^{T}B^{T}=BA-AB=-(AB-BA)$, so it is skew-symmetric. Hence the third statement is correct.
An invertible square matrix has a unique inverse, so the statement saying it may have more than one inverse is false.
final answer: If a square matrix is invertible, then it may have more than one inverse.