Determine if the statement is true or false, and justify your answer.

a. Every matrix A has a determinant.

b. Every nonsquare matrix has a determinant, but square matrices do not.

c. Every square matrix has a determinant, but nonsquare matrices do not.

d. If every entry in a matrix is zero, then the determinant is undefined.

e. If every entry in a matrix is one, then the determinant is undefined.

Step-by-step explanation:

a) False. A rectangular matrix cannot have a determinant only square matrices can have determinants

b) False. Only square matrices have determinants and non square matrices do not have

c) True.

d) False. If it is a square matrix and every entry is 0 then determinant = 0

e) False. If it is a square matrix determinant = 0 since when two rows are identical the determinant value is 0.