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Question
Mathematics
The number of elements in the set A = beginpmatrix a b 0 d endpmatrix: a , b , d β -1,0,1 text and ( I - A )3= I - A 3 where I is 2 Γ 2 identity matrix, is :
Q. The number of elements in the set
{
A
=
(
a
0
β
b
d
β
)
:
a
,
b
,
d
β
{
β
1
,
0
,
1
}
Β andΒ
(
I
β
A
)
3
=
I
β
A
3
}
where I is
2
Γ
2
identity matrix, is :
4318
216
JEE Main
JEE Main 2021
Matrices
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Answer:
8
Solution:
(
I
β
A
)
3
=
I
3
β
A
3
β
3
A
(
I
β
A
)
=
I
β
A
3
β
3
A
(
I
β
A
)
=
0
Β orΒ
A
2
=
A
β
[
a
2
0
β
ab
+
b
d
d
2
β
]
=
[
a
0
β
b
d
β
]
β
a
2
=
a
,
b
(
a
+
d
β
1
)
=
0
,
d
2
=
d
If
b
ξ
=
0
,
a
+
d
=
1
β
4
ways
If
b
=
0
,
a
=
0
,
1&
d
=
0
,
1
β
4
ways
β
Total
8
matrices