Linear Algebra - 2.2

Linear Algebra - 2.2 Questions and Answers 2023. In order for a matrix B to be an inverse of A, both equations AB = I and BA = I must be true Correct Answer: True If A and B are n x n and invertible, then A^-1B^-1 is the inverse of AB Correct Answer: False. The inverse of two invertible matrices is the reverse of their individual matrices inverted If A = [a b] and ab - cd does [c d] not equal zero, then A is invertible Correct Answer: False. Then the statement would be contrapositive to the statement in Thm 4. AD not AB If A is an invertible n x n matrix, then the equation Ax = b is consistent for each b in Rn Correct Answer: True Each elementary matrix is invertible Correct Answer: True A product of invertible n x n matrices is invertible, and the inverse of the product is the product of their inverses in the same order Correct Answer: False, it is invertible, but the inverses in the product of the inverses in the reverse order If A is invertible, then the inverse of A^-1 is A itself Correct Answer: True If A = [a b] [c d] and ad = bc, then A is not invertible Correct Answer: True (A^-1)^-1 Correct Answer: A (AB)^-1 Correct Answer: B^-1*A^-1 (A^T)^-1 Correct Answer: (A^-1)^T (ABCD)^-1 Correct Answer: A^-1B^-1C^-1D^-1