###### Exercise5

Determine whether the following statements are true or false and explain your response.

1. If we have a square matrix $$A$$ and multiply the first row by $$5$$ and add it to the third row to obtain $$A'\text{,}$$ then $$\det A' = 5\det A\text{.}$$

2. If we interchange two rows of a matrix, then the determinant is unchanged.

3. If we scale a row of the matrix $$A$$ by $$17$$ to obtain $$A'\text{,}$$ then $$\det A' = 17\det A\text{.}$$

4. If $$A$$ and $$A'$$ are row equivalent and $$\det A' = 0\text{,}$$ then $$\det A = 0$$ also.

5. If $$A$$ is row equivalent to the identity matrix, then $$\det A = \det I = 1\text{.}$$

in-context