4. (9 points) Give examples of A and B such that(a) A B is not invertible although A and B are invertible.(b) A B is invertible although A and B are not invertible(c) All of A, B and A B are invertible.(d) In the last case, show that B^-1 A^-1 is also invertible and find a formula for its inverse.(Hint: Check this out A^-1(A B)B^-1)

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Let TA: R^n →R^n be multiplication by an invertible matrix A, and let {𝐮1, 𝐮2, …, 𝐮n} be a basis for R^n . Prove that {T1(ℍ1)1 T1(ℕ2)1, …, N1(𝐈n)} is also a hasis for R^n | Numerade

If 'A' is an invertible matrix of order 2, then det (A-1) is equal to. - | Shaalaa.com

Suppose A is invertible and you exchange its first two rows to reach B. Is the new matrix B invertible? How would you find B^-1 from A^-1 ? | Numerade