1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Definition of a Determinant
If B is an id...
Question
If B is an idempotent matrix, and
A
=
I
−
B
, then
A
A
2
=
A
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
A
2
=
I
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
A
B
=
0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
B
A
=
0
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct options are
A
A
2
=
A
C
A
B
=
0
D
B
A
=
0
Property of Idempotent matrix
B
2
=
B
A
=
I
−
B
Multiply with B on both sides.
B
A
=
B
I
−
B
2
B
A
=
B
−
B
=
0
Hence
B
A
=
0
=
A
B
A
=
I
−
B
⇒
A
A
=
A
I
−
A
B
⇒
A
2
=
A
−
A
B
As
A
B
=
0
A
2
=
A
−
0
⇒
A
2
=
A
Suggest Corrections
0
Similar questions
Q.
A square matrix
A
is said to be an idempotent matrix if
A
2
=
A
.
If
A
and
B
are idempotent matrices and
A
B
=
B
A
, then which of the following is an idempotent matrix
Q.
A square matrix
A
is said to be an idempotent matrix if
A
2
=
A
and
B
=
I
−
A
, then
Q.
If
A
is a square matrix such that
A
2
=
A
and
B
=
I
−
A
, then
A
B
+
B
A
+
I
−
(
I
−
A
)
2
is equal to.
Q.
A square matrix
A
is said to be an idempotent matrix if
A
2
=
A
.
If
A
,
B
and
A
+
B
are idempotent matrices, then
Q.
If
A
is an idempotent matrix and
(
2
I
+
A
)
4
=
a
I
+
b
A
,
(
I
is unit matrix
)
,
a
,
b
∈
R
.
Then
(
a
+
b
)
=
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
Related Videos
Introduction
MATHEMATICS
Watch in App
Explore more
Definition of a Determinant
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