True or false: inverses

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   If AB = BA = I then B is the inverse of A.

2. Statement is true

   Yes

   Statement

   An inverse, when it exists, is unique.

3. Statement is true

   No

   Statement

   Every square matrix has an inverse.

4. Statement is true

   Yes

   Statement

   If B is the inverse of A then A is the inverse of B.

5. Statement is true

   No

   Statement

   A matrix can have two distinct inverses.

Explanation