MathDB
Problems
Contests
National and Regional Contests
Romania Contests
District Olympiad
2024 District Olympiad
P1
Simple 2x2 matrix
Simple 2x2 matrix
Source: Romanian District Olympiad 2024 11.1
March 10, 2024
linear algebra
matrix
Problem Statement
Consider the matrix
X
∈
M
2
(
C
)
X\in\mathcal{M}_2(\mathbb{C})
X
∈
M
2
(
C
)
which satisfies
X
2022
=
X
2023
.
X^{2022}=X^{2023}.
X
2022
=
X
2023
.
Prove that
X
2
=
X
3
.
X^2=X^3.
X
2
=
X
3
.
Back to Problems
View on AoPS