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Byju's Answer
Standard XII
Mathematics
Evaluation of a Determinant
Let A be a 2 ...
Question
Let
A
be a
2
×
2
matrix with det
(
A
)
=
−
1
and det
(
(
A
+
I
)
(
Adj
(
A
)
+
I
)
)
=
4
. Then the sum of the diagonal elements of
A
can be
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Solution
|
(
A
+
I
)
(
adj
A
+
I
)
|
=
4
⇒
|
A
adj
A
+
A
+
adj
A
+
I
|
=
4
⇒
|
(
A
)
|
I
+
A
+
adj
A
+
I
|
=
4
|
A
|
=
–
1
⇒
|
A
+
adj
A
|
=
4
A
=
[
a
b
c
d
]
adj
A
=
[
a
−
b
−
c
d
]
⇒
[
(
a
+
d
)
0
0
(
a
+
d
)
]
=
4
⇒
a
+
d
=
±
2
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59
Similar questions
Q.
Let
A
be a
3
×
3
real matrix. If
det
(
2 Adj(2 Adj(Adj(2A)))
)
=
2
41
,
then the value of
det
(
A
2
)
equals
Q.
Assertion :
Let
A
be a
2
×
2
matrix with real entries. Let
I
be the
2
×
2
identity matrix. Denote by
t
r
(
A
)
, the sum of diagonal entries of
A
. Assume that
A
2
=
I
.
If
A
≠
I
and
A
≠
−
I
, then
d
e
t
(
A
)
=
−
1
.
Reason: If
A
≠
I
and
A
≠
−
I
, then
t
r
(
A
)
≠
0
.
Q.
Let
A
be a matrix of order
3
×
3
and det
(
A
)
=
2.
Then
det
(
det
(
A
)
adj
(
5
adj
(
A
3
)
)
)
is equal to
Q.
Let A be a
2
×
2
matrix with real entries. Let I be the
2
×
2
identity matrix. Denote by tr(A), the sum of diagonal entries of
A
. Assume that
A
2
=
I.
Statement-l: If
A
≠
I
and
A
≠
−
I
, then
det
A
=
−
1
.
Statement-2: If
A
≠
I
and
A
≠
−
I
, then
t
1
{
A
)
≠
0
.
Q.
Let
A
be a
2
×
2
matrix with real entries, Let I be the
2
×
2
identity matrix. Denote by
t
r
(
A
)
,
the sum of diagonal entries of
A
. Assume that
A
2
=
I
Statement
1
:
If
A
≠
I
and
A
≠
−
I
, then det
A
=
−
1
Statement
2
:
If
A
≠
I
and
A
≠
−
I
, then
t
r
(
A
)
≠
0
,
then which of the following is correct
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