MATH 4C Linear Algebra Chapter 2 TRUE OR FALSE

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

FALSE; B^-1A^-1 is the inverse of AB.

T/F - If A = [a, b, c, d] and ab - cd cannot equal 0, then A is inveritble.

FALSE; if ad - bc cannot equal 0, then A is invertible.

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

TRUE; by definition

T/F - If A is an invertible n x n matrix, then the equation Ax = b is consistent for each b in R^n.

TRUE; since A is invertible, A^-1b exists for all b in R^n. Define x = (A^-1)b. Then Ax = b.

Each elementary matrix is invertible.

TRUE; since each elementary matrix corresponds to a row operation, and every row operation is reversible, every elementary matrix has an inverse matrix.