Question 26 - Week 7 Practice | Prasnya
Prasnya
Continue with Google
Practice route
Week 7
Field
IITM-DS
Exam
Quiz 2
Subject
Mathematics 2
Week
Week 7
Question 26 of 43
Practice question
00:00
Est. 3 min
Marks
+3.00
0.00
Question
Let
A
A
and
B
B
be
n
×
n
n\times n
matrices. Which statements are true?
Multiple correct
Medium Difficulty
03 December 2023
A
If
A
A
and
B
B
are similar, then the nullity of
A
A
and the nullity of
B
B
are equal.
B
Let
A
A
and
B
B
be similar matrices. Then
A
x
=
0
Ax=0
has a unique solution if and only if
B
x
=
0
Bx=0
has a unique solution.
C
If
A
k
A^k
and
B
k
B^k
are similar for some positive integer
k
k
, then
A
A
and
B
B
are similar.
D
If
A
A
and
B
B
are similar matrices where
A
A
is a scalar matrix, then
A
=
B
A=B
.
