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Binomial theorem for commuting matrices
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Mathematics
Area of mathematics
Combinatorics
Binomial coefficient
Binomial theorem
Created
2026-09-24
Updated
2026-10-03
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If
square matrices
A
and
B
commute, then
(
A
+
B
)
n
=
∑
k
=
0
n
(
k
n
)
A
n
−
k
B
k
.
(1)
The usual proof
works
because commutativity allows
words
with the same
numbers
of
A
and
B
factors to be collected.
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Binomial theorem
Binomial coefficient
Combinatorics
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2021
/
ib
/
Paper 1
/
8E
/
a
/
ii
/
Solution
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