Question

In order for a matrix B to be the inverse of A, both equations AB=1 and BA=I must be true.

A. True, by definition of invertible. OB.
B. False; if AB=1 and BC = 1, then A is one inverse of B and C is possibly another inverse of B.
C. True; since AB=BA, AB=l if and only if BA=I.
D. False; it's possible that the product AB is defined and equals I, yet the product BA is not defined.

Answer 1

The correct answer is D. False; it's possible that the product AB is defined and equals I, yet the product BA is not defined.

Step-by-step explanation:

Answer:

The correct answer is D. False; it's possible that the product AB is defined and equals I, yet the product BA is not defined.

For a matrix B to be the inverse of matrix A, both equations AB=1 and BA=I must be true. However, it is possible that the product AB is defined and equals the identity matrix I, while the product BA is not defined. This means that not every matrix A has an inverse matrix.

Therefore, option D is the correct answer.