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The Pauli spin matrices in quantum mechanics are0ABC=-10Show that A2B2C2 = 1.a)-BAb)Show that ABShow that AB BA 2iC

Question
The Pauli spin matrices in quantum mechanics are
0
A
B
C
=
-1
0
Show that A2
B2
C2 = 1.
a)
-BA
b)
Show that AB
Show that AB BA 2iC
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The Pauli spin matrices in quantum mechanics are 0 A B C = -1 0 Show that A2 B2 C2 = 1. a) -BA b) Show that AB Show that AB BA 2iC

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check_circleAnswer
Step 1

a)

For matrix A

0 10 1
A2
1
0
1
0
0 1 0 0
0 0 1+0
1 0
0 1
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0 10 1 A2 1 0 1 0 0 1 0 0 0 0 1+0 1 0 0 1

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Step 2

For matrix B

 

0
0 -i
0-i
В?
i
0
0-i2 0+0
0+0 i0
1 0
0 1
= I
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0 0 -i 0-i В? i 0 0-i2 0+0 0+0 i0 1 0 0 1 = I

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Step 3

For matrix C

 ...

1
C2
0
1
0
0 -1
-1
1+0 0 0
0 0 0+1
1 0
0
1
- 1
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1 C2 0 1 0 0 -1 -1 1+0 0 0 0 0 0+1 1 0 0 1 - 1

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