Which are true for any square matrix A a If detA notequalto

Which are true for any square matrix A? a) If det(A) notequalto 0 then Ax = 0 has only the trivial solution. b) If A is square and Ax = 0 has only the trivial solution then Ax = b has one and only one solution no matter what b is. c) det(A) notequalto 0 then the reduced row echelon form of A is the identity matrix. d) Every square matrix can be written as a product of elementary matrices. e) If det(A) = 0 then A does not have an ineverse.

Solution

a) false

b) it is true if b=0 otherwise false

c) false (may or may not identity matrix)

d) true

e) true