Analyze Option A: \((A + B)^{-1} = B^{-1} + A^{-1}\). This statement is generally incorrect. The inverse of a sum of matrices is not the sum of their inverses.
Analyze Option B: \((AB)^{-1} = B^{-1} A^{-1}\). This statement is a fundamental property of invertible matrices and is correct.
Analyze Option C: \(\text{adj}(A) = |A| A^{-1}\). This statement is the definition of the adjoint of a matrix and is correct.
Analyze Option D: \(|A^{-1}| = |A|^{-1}\). This statement is a property of the determinant of an inverse matrix and is correct.
AI generated content. Review strictly for academic accuracy.
Pedagogical Audit
Bloom's Analysis:
This is an APPLY question because the student needs to apply the properties of invertible matrices to identify the incorrect statement.
Knowledge Dimension:CONCEPTUAL
Justification:The question requires understanding the concepts of matrix inverses, adjoints, and determinants, rather than just recalling facts.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests knowledge of matrix algebra and properties of inverse matrices as covered in the textbook.