True or false? 3. The determinant of an elementary matrix is never zero.

Expert Answers
rakesh05 eNotes educator| Certified Educator


Because elementary matrices are a result  of identity matrices by applying elementary operations. Also an elementary matrix is invertible. And as determinant of an identity matrix is 1`!=0` . Hence the determinant of elementary matrices is non-zero.

pramodpandey | Student


If E is an elementary matrix, then E is invertible i.e `E^(-1)` exist. Hence