A set of rules in my textbook is as follows:
a. If $A$ has a zero row (column), then $\det A = 0$
b. If $B$ is obtained by interchanging two rows (columns) of $A$, then $\det B = -\det A$
c. If $A$ has two identical rows (columns), then $\det A = 0$
d. If $B$ is obtained by multiplying a row (column) of $A$ by $k$, then $\det B = k\cdot\det A$
e. If $A$, $B$, and $C$ are identical except that the $i$-th row (column) of $C$ is the sum of the $i$-th rows (columns) of $A$ and $B$, then $\det C = \det B + \det A$
f. If $B$ is obtained by adding a multiple of one row (column) of $A$ to another row (column), then $\det B = \det A$
I don't understand why "column" is in parentheses after every instance of row. Is that the same as saying, for example with clause a: "if $A$ has a zero row or a zero column, then $\det A = 0$"? As in, it's saying that column and row can be used interchangably in the statement, as the statement holds true either way?
If the above interpretation is correct, then how? Why would these statements that apply to rows also apply to columns. The only situation I could see it applying is if the matrix is symmetrical, but the question doesn't specify that, it only says that the matrix is square.
Any help is appreciated.