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Byju's Answer
Standard XII
Mathematics
Inverse of a Matrix
If A3 = 0 t...
Question
If
A
3
=
0
then
1
+
A
+
A
2
is equal to
A
I + A
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B
(
I
+
A
)
−
1
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C
I - A
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D
(
I
−
A
)
−
1
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Solution
The correct option is
D
(
I
−
A
)
−
1
since the eigenvalue of matrix
A
is zero
(
I
−
A
)
is invertible we have
(
I
−
A
)
(
I
+
A
+
A
2
)
=
I
−
A
3
=
I
−
0
=
I
(
I
−
A
)
(
I
+
A
+
A
2
)
=
I
∴
I
+
A
+
A
2
=
(
I
−
A
)
−
1
Suggest Corrections
0
Similar questions
Q.
If
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=
0
, then
I
+
A
+
A
2
equals
Q.
If
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Then
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equals :-
Q.
If
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If
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,
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.
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>
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for all
i
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√
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√
a
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2
+
√
a
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+
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.
+
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Q.
A square matrix A is said to be nilpotent of index m. If
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=
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(
I
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2
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