5
You visited us
5
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Combination
If A is a nil...
Question
If
A
is a nilpotent matrix of index
2
,
then for any positive integer
n
,
A
(
I
+
A
)
n
is equal to
A
A
−
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
A
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
A
n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
I
n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
B
A
Given that
A
is a nilpotent matrix of index
2
A
2
=
O
,
A
3
=
A
4
=
⋯
=
A
n
=
O
Then,
A
(
I
+
A
)
n
=
A
(
I
+
n
A
)
=
A
+
n
A
2
=
A
Suggest Corrections
1
Similar questions
Q.
If
A
is a nilpotent matrix of index
2
, then for any positive integer
n
,
A
(
I
+
A
)
n
is equal to
Q.
If
A
is a square matrix such that
|
A
|
=
2
, then for any positive integer
n
,
|
A
n
|
is equal to
Q.
If
(
2
4
−
1
k
)
is a nilpotent matrix of index
2
,
then
k
equals to
Q.
A square matrix A is said to be a nilpotent matrix of degree
r
, if
r
is the least positive integer such that
A
r
=
0
. If
A
and
B
are nilpotent matrices then
A
+
B
will be a nilpotent matrix if
Q.
A square matrix A is said to be nilpotent of index m. If
A
m
=
0
, now, if for this A,
(
I
−
A
)
n
=
I
+
A
+
A
2
+
A
3
+
.
.
.
.
+
A
m
−
1
, then n is equal to?
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Explore more
Combination
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app