MathDB

IMC 2011 Day 1 Problem 2

Source:

July 30, 2011

linear algebramatrixalgebrapolynomialfunctionlinear algebra unsolved

Problem Statement

Does there exist a real

3\times 3

matrix

A

such that

\text{tr}(A)=0

and

A^2+A^t=I?

(

\text{tr}(A)

denotes the trace of

A,\ A^t

the transpose of

A,

and

I

is the identity matrix.)
Proposed by Moubinool Omarjee, Paris