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SEEMOUS
2021 SEEMOUS
Problem 2
Problem 2
Part of
2021 SEEMOUS
Problems
(1)
Commutative implies non-negative determinant
Source: 2021 SEEMOUS, P2
7/23/2021
Let
n
≥
2
n \ge 2
n
≥
2
be a positive integer and let
A
∈
M
n
(
R
)
A \in \mathcal{M}_n(\mathbb{R})
A
∈
M
n
(
R
)
be a matrix such that
A
2
=
−
I
n
A^2=-I_n
A
2
=
−
I
n
. If
B
∈
M
n
(
R
)
B \in \mathcal{M}_n(\mathbb{R})
B
∈
M
n
(
R
)
and
A
B
=
B
A
AB = BA
A
B
=
B
A
, prove that
det
B
≥
0
\det B \ge 0
det
B
≥
0
.
linear algebra