Final answer:
The statement that every elementary matrix is invertible is true, as elementary row operations are reversible, thus guaranteeing the existence of an inverse for each elementary matrix.
Step-by-step explanation:
The statement "Each elementary matrix is invertible" is true. An elementary matrix is found out by performing single elementary row operation on an identity matrix. Such operations include swapping two rows, multiplying a row by a nonzero scalar, or adding a multiple of one row to another row.
Because each of these operations is reversible, the resulting elementary matrix can always be transformed back into the original identity matrix. Therefore, the inverse exists for each elementary matrix, verifying the statement as true.