CUET Preparation Today
Which of the following is NOT correct? |
If matrix B is the inverse of matrix A, then A is the inverse of B. A rectangular matrix of order $m×n,m≠n$ does not possess an inverse. If A and B are symmetric matrices of the same order, then (AB-BA) is a skew-symmetric matrix. If a square matrix is invertible, then it may have more than one inverse. |
If a square matrix is invertible, then it may have more than one inverse. |
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. |
