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consider the group g a m2 aat i2 with respect to m
Question:
Consider the group G = {A ∈ M
2
(ℝ): AA
T
= I
2
} with respect to matrix multiplication. Let
Z(G) = {A ∈ G : AB = BA, for all B ∈ G}.
Then, the cardinality of Z(G) is
IIT JAM MA - 2023
IIT JAM MA
Updated On:
Dec 18, 2024
1
2
4
infinite
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The Correct Option is
B
Solution and Explanation
The correct option is (B) : 2.
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Top Questions on Groups
Consider
𝐺
=
{
𝑚
+
𝑛
2
∶
𝑚
,
𝑛
∈
Z
}
𝐺 = \left\{𝑚 + 𝑛\sqrt2\ ∶\ 𝑚, 𝑛 ∈ \Z\right\}
G
=
{
m
+
n
2
∶
m
,
n
∈
Z
}
as a subgroup of the additive group ℝ.
Which of the following statements is/are TRUE ?
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y
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z
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z
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x
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y
,
z
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2
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y
2
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z
2
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a
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1
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1
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2
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2
3
1
0
1
2
2
1
0
1
3
2
1
0
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th
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