Linear Algebra - 2.2

(A^T)^-1

(A^-1)^T

(A^-1)^-1

A

(ABCD)^-1

A^-1B^-1C^-1D^-1

(AB)^-1

B^-1*A^-1

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

False, it is invertible, but the inverses in the product of the inverses in the reverse order

If A and B are n x n and invertible, then A^-1B^-1 is the inverse of AB

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

False. Then the statement would be contrapositive to the statement in Thm 4. AD not AB

Each elementary matrix is invertible

True

If A = [a b] [c d] and ad = bc, then A is not invertible

True

If A is an invertible n x n matrix, then the equation Ax = b is consistent for each b in Rn

True

If A is invertible, then the inverse of A^-1 is A itself

True

In order for a matrix B to be an inverse of A, both equations AB = I and BA = I must be true

True