Solution
= Solution
The scalar multiplication $\lambda A$ multiplies every one of the $n$ rows by $\lambda$. Applying <multilinearity of the determinant> once to each row gives
$$
\boxed{\det(\lambda A)=\lambda^n\det A}.
$$
= Solution
The scalar multiplication $\lambda A$ multiplies every one of the $n$ rows by $\lambda$. Applying <multilinearity of the determinant> once to each row gives
$$
\boxed{\det(\lambda A)=\lambda^n\det A}.
$$