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IMC
2024 IMC
3
3
Part of
2024 IMC
Problems
(1)
Can a 0-1 matrix square to the matrix with all ones?
Source: IMC 2024, Problem 3
8/7/2024
For which positive integers
n
n
n
does there exist an
n
×
n
n \times n
n
×
n
matrix
A
A
A
whose entries are all in
{
0
,
1
}
\{0,1\}
{
0
,
1
}
, such that
A
2
A^2
A
2
is the matrix of all ones?
linear algebra
matrix
Square matrix