Question:medium
If \( A \) and \( B \) are invertible matrices, then which of the following is not correct?
If \( A \) and \( B \) are invertible matrices, then which of the following is not correct?
Show Hint
Matrix inverse operations follow specific rules. For addition, the inverse of a sum is not the sum of the inverses.
Updated On: Feb 25, 2026
- \( (A + B)^{-1} = B^{-1} + A^{-1} \)
- \( (AB)^{-1} = B^{-1} A^{-1} \)
- \( \text{adj} = |A| A^{-1} \)
- \( |A|^{-1} = |A^{-1}| \)
Show Solution
The Correct Option is A
Solution and Explanation
The equation \( (A + B)^{-1} = B^{-1} + A^{-1} \) is erroneous. Matrix addition and matrix multiplication do not follow the same rules; therefore, the inverse of the sum of two matrices is not equivalent to the sum of their individual inverses.
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