Solution
= Solution
Every column has $n$ entries of magnitude at most one, so $\|a_j\|^2\leq n$. Substituting in part (d) gives
$$
\boxed{|\det A|\leq\prod_{j=1}^n\sqrt n=n^{n/2}.}
$$
The bound comes from the maximum allowed column lengths, together with Hadamard's inequality.