Let A, B, and C be matrices such that the products AB, AC, and BA exist. Which o

ID: 3104236 • Letter: L

Question

Let A, B, and C be matrices such that the products AB, AC, and BA exist. Which one of the following statements is NOT true?

a. Let x and b be n x 1 matrices. If A is an n x n matrix but A is not invertible, then the linear equation Ax = b has no solution for x.

b. If A is invertible, then its inverse A-1 exists and (A-1)-1 = A.

c. If A and B are invertible matrices of the same size, then AB is invertible and (AB)-1 = B-1A-1.

d. For every scalar k 0, if A is invertible, then kA is also invertible and (kA)-1 = (1/k)A-1.

e. If AB = AC and A is invertible, then B = C.

f. AB is not equal to BA in general.

a is NOT True

b is True

C is True

d is true

e is true

f is true

only a is not true remaining all are true.

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