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

Answer 1

(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