True or false: adjoint and inverse

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   A (adj A) = (adj A) A = |A| I.

2. Statement is true

   Yes

   Statement

   adj A is the transpose of the matrix of cofactors.

3. Statement is true

   No

   Statement

   Every square matrix has an inverse.

4. Statement is true

   Yes

   Statement

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

5. Statement is true

   Yes

   Statement

   (A⁻¹)⁻¹ = A.

6. Statement is true

   No

   Statement

   A singular matrix still has an inverse.

Explanation