2.2 The Inverse of a Matrix(T/F)

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

If A = {a,b; c,d} and ab-cd != 0 then A is invertible

False

If A and B are nxn and invertible, then inv(A)inv(B) is the inverse of AB.

False

If A is invertible, then the elementary row operations that reduce A to the identity In also reduce inv(A) to In

False

Each elementary matrix is invertible

True

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

True

If A can be row reduced to the identity matrix, then A must be 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 inv(A) is A itself.

True

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

True