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Byju's Answer
Standard XII
Mathematics
Intersection
If I3 denotes...
Question
If I
3
denotes identity matrix of order 3 × 3, write the value of its determinant.
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Solution
In an identity matrix, all the diagonal elements are 1 and rest of the elements are 0.
Here,
I
3
=
1
0
0
0
1
0
0
0
1
=
1
×
1
0
0
1
Expanding
along
C
1
=
1
⇒
I
3
=
1
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Similar questions
Q.
If
I
3
is the identity matrix of order
3
, then
(
I
3
)
−
1
is
Q.
If |A| denotes the value of the determinant of a square matrix of order 3, then |–2A| = ___________.
Q.
A matrix of order 3 × 3 has determinant 2. What is the value of |A (3I)|, where I is the identity matrix of order 3 × 3.
Q.
Let
P
=
⎡
⎢
⎣
−
30
20
56
90
140
112
120
60
14
⎤
⎥
⎦
and
A
=
⎡
⎢
⎣
2
7
ω
2
−
1
−
ω
1
0
−
ω
−
ω
+
1
⎤
⎥
⎦
where
ω
=
−
1
+
i
√
3
2
and
I
3
be the identity matrix of order 3. If the determinant of the matrix
(
P
−
1
A
P
−
I
3
)
2
is
α
ω
2
, then the value of
α
is equal to
Q.
If
A
=
⎡
⎢
⎣
1
2
2
2
1
2
2
2
1
⎤
⎥
⎦
and
A
2
−
4
A
=
k
I
3
, then find the value of
k
.
[Where
I
3
is the identity matrix of order
3
]
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