If A and B are invertible matrices, then which of the following is not correct? - Mathematics

प्रश्न

If A and B are invertible matrices, then which of the following is not correct?

विकल्प

adj A = |A|.A^–1
det(A)^–1 = [det(A)]^–1
(AB)^–1 = B^–1A^–1
(A + B)^–1 = B^–1 + A^–1

MCQ

उत्तर

(A + B)^–1 = B^–1 + A^–1

Explanation:

If A and B are two invertible matrices then

(a) adj A = |A| · A^–1 is correct

(b) det (A)^–1 = [det(A)]^–1 = $\frac{1}{det (A)}$ is correct

(d) (A + B)^–1 = $\frac{1}{| A + B |} \cdot adj (A + B)$

∴ (A + B)^–1 ≠ B^–1 + A^–1

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Inverse of Matrix - Inverse of a Square Matrix by the Adjoint Method

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Q 34 Q 33 Q 35

अध्याय 4: Determinants - Exercise [पृष्ठ ८२]

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अध्याय 4 Determinants
Exercise | Q 34 | पृष्ठ ८२

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If A and B are invertible matrices, then which of the following is not correct? - Mathematics

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If A and B are invertible matrices, then which of the following is not correct? - Mathematics

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