# Understand the problem

Let \(S=\{x \in \Bbb R| x=tr(A)\) for some \(A \in M_4(\Bbb R)\) s.t \(A^2=A\}\)

#### Then which of the following will describe \(S\):

- \(S=\{0,2,4\}\)
- \(S=\{0,1/2,1,3/2,2,5/2,3,7/2,4\}\)
- \(S=\{0,1,2,3,4\}\)
- \(S=[0,4]\)

##### Source of the problem

TIFR 2019 GS Part A, Problem 10

##### Topic

Linear algebra

##### Difficulty Level

Moderate

##### Suggested Book

Linear algebra by Friedbarg

# Start with hints

Do you really need a hint? Try it first!

What can you say about the minimal polynomial of ?

Observe that min poly. Then the minimal poly could be..?

Can you construct the matrix now?

The matrix corresponding to is zero matrix and the identity matrix respectively and what are the matrices corresponding to ?

Can you think about option 3)?

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