Invert a sequence of row operations

mark

Let $S$ denote the sequence of row operations $R_{2,4}(3R_4+R1)(2R_2)$. Express $S^{-1}$ as a sequence of row operations.

Student23

$$
S^{-1} = R_{4,2}(-3R_4 + R_1)(\frac{1}{2}R_2)
$$

mark

@Student23 said:
$$
S^{-1} = R_{4,2}(-3R_4 + R_1)(\frac{1}{2}R_2)
$$

This is close but missing an important element. You clearly know how to invert each single row operation but I don't think you've quite got the correct approach to dealing with a sequence of row operations.

Student23

Would the order of the row operations need to be reversed since $S^{-1}$ is the inverse of the sequence? Making the sequence look like:
$$
S^{-1} = (\frac{1}{2}R_2)(-3R_4 + R_1)R_{4,2}
$$