Solution
= Solution
Multiplying $A$ by $c$ multiplies each of its $n$ columns by $c$. The <multilinearity> of the <determinant> therefore gives
$$
\boxed{\det(cA)=c^n\det A.}
$$
This includes $c=0$.
= Solution
Multiplying $A$ by $c$ multiplies each of its $n$ columns by $c$. The <multilinearity> of the <determinant> therefore gives
$$
\boxed{\det(cA)=c^n\det A.}
$$
This includes $c=0$.