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

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### 2 Answers

True.

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.

True.

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

`det(E.E^(-1))=det(I_n)=1`

`det(E).det(E^(-1)=1`

`det(E)!=0`