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Question
If A and B are invertible matrices, then which of the following is not correct?
Options
adj A = |A|.A–1
det(A)–1 = [det(A)]–1
(AB)–1 = B–1A–1
(A + B)–1 = B–1 + A–1
Solution
(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 = `1/("det"("A"))` is correct
(c) Also, (AB)–1 = B–1A–1 is correct
(d) (A + B)–1 = `1/|"A" + "B"| * "adj"("A" + "B")`
∴ (A + B)–1 ≠ B–1 + A–1
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