If `A`
and `B`
are invertible
matrices, which of the following statement is not correct.
`a d j\ A=|A|A^(-1)`
(b) `det(A^(-1))=(detA)^(-1)`
(c) `(A+B)^(-1)=A^(-1)+B^(-1)`
(d) `(A B)^(-1)=B^(-1)A^(-1)`
Text Solution
AI Generated Solution
To determine which statement is not correct among the given options regarding invertible matrices \( A \) and \( B \), let's analyze each statement step by step.
### Step-by-Step Solution:
1. **Statement (a):** \( \text{adj}\ A = |A| A^{-1} \)
- This statement is a known property of matrices. The adjoint (or adjugate) of a matrix \( A \) is equal to the determinant of \( A \) multiplied by the inverse of \( A \).
- **Conclusion:** This statement is **correct**.
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Knowledge Check
If A, B, C are invertible matrices, then (ABC)^(-1) =
A
`A^(-1)B^(-1)C^(-1)`
B
`C^(-1)A^(-1)B^(-1)`
C
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D
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Which one of the following is correct? If (1)/(b-c)+(1)/(b-a)=(1)/(a)+(1)/(c), then a, b, c are in
A
AP
B
HP
C
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D
None of these
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