1988 Putnam A6

If a linear transformation $A$ on an $n$-dimensional vector space has

$n+1$ eigenvectors such that any $n$ of them are linearly independent,

does it follow that $A$ is a scalar multiple of the identity? Prove

your answer.

如果 $n$ 维向量空间上的线性变换 $A$ 有

$n+1$ 个特征向量，其中任何 $n$ 都是线性无关的，

是否可以得出 $A$ 是恒等式的标量倍数？证明

你的答案。