# Elementary Matrix and Elementary Operation and Invertibility

Please check my understanding is correct:

1. Elementary Matrix is obtained by only 1 row/column operation from Identity Square Matrix.

2. Elementary matrices are invertible, however, not all invertible matrices are elementary matrices.

3. All invertible matrices colud be represented by(decomposed to) the multiplication of elementary matrices.

• Yes, this is correct. – Chris Jun 5 '17 at 4:53
• How do 1 column operations work? Replacing the $k$th column by any other? – draks ... Jun 7 '17 at 5:43