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Byju's Answer
Standard XII
Mathematics
Cube Root of a Complex Number
Let fx = 1 ...
Question
Let
f
(
x
)
=
1
+
x
1
−
x
. If A is matrix for which
A
3
=
O
, then
f
(
A
)
is
A
I
+
A
+
A
2
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B
I
+
2
A
+
2
A
2
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C
I
−
A
−
A
2
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D
none of these
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Solution
The correct option is
B
I
+
2
A
+
2
A
2
f
(
x
)
=
1
+
x
1
−
x
=
(
1
+
x
)
(
1
+
x
+
x
2
)
(
1
−
x
)
(
1
+
x
+
x
2
)
=
1
+
2
x
+
2
x
+
x
3
1
−
x
3
∴
f
(
A
)
=
1
+
2
A
+
2
A
2
+
A
3
1
−
A
3
=
1
+
2
A
+
2
A
2
, since
A
3
=
O
Suggest Corrections
0
Similar questions
Q.
Let
f
(
x
)
=
1
+
x
1
−
x
.
If
A
is matrix for which
A
3
=
O
,
then
f
(
A
)
is
Q.
If
A
3
=
0
, then
I
+
A
+
A
2
equals
Q.
Let A be a
3
×
3
matrix such that
A
2
−
5
A
+
7
I
=
O
Statement I:
A
−
1
=
1
7
(
5
I
−
A
)
Statement II: The polynomial
A
3
−
2
A
2
−
3
A
+
I
can be reduced to
5
(
A
−
4
I
)
Then:
Q.
For a square matrix
A
,
if
A
3
=
O
,
then
I
+
A
+
A
2
is equal to
Q.
If a matrix A is such that 3
A
3
+
2
A
2
+
5
A
+
I
=
0
,
then
A
-
1
equal to
(a)
-
3
A
2
+
2
A
+
5
(b)
3
A
2
+
2
A
+
5
(c)
3
A
2
-
2
A
-
5
(d) none of these
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