# A multiple choice question for complex matrix [closed]

Let $A$ be an $n \times n$ matrix with complex entries. Pick out the true statements.

1. $A$ is always similar to an upper-triangular matrix.
2. $A$ is always similar to a diagonal matrix.
3. $A$ is similar to a block diagonal matrix, with each diagonal block of size strictly less than $n$, provided $A$ has at least $2$ distinct eigenvalues.

I have solved $1$ & $2$. $1$ is true and $2$ is false.

But I cannot find how to solve $3$. Can somebody help?

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## closed as off-topic by Michael Albanese, Dr. MV, BLAZE, Claude Leibovici, Jyrki Lahtonen♦Dec 11 '15 at 9:50

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• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Michael Albanese, Dr. MV, BLAZE, Claude Leibovici, Jyrki Lahtonen
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