Question 42 - Week 1 Practice | Prasnya
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Week 1
Question 42
00:00
Est. 3 min
Marks:
+2.00
0.00
Choose the set of correct options.
Multiple correct
Medium Difficulty
16 October 2022
A
If there is a square matrix
A
A
such that
A
2
−
A
=
0
A^2-A=0
, then
det
(
A
)
\det(A)
must be either
0
0
or
−
1
-1
.
B
If
u
u
is a solution of the system of linear equations
A
x
=
c
Ax=c
and
c
c
is a solution of the system of linear equations
A
x
=
b
Ax=b
, then
u
u
is a solution of the system of linear equations
A
2
x
=
b
A^2x=b
.
C
If
B
B
is a scalar matrix of order
3
3
, then
A
B
−
B
A
=
0
AB-BA=0
for all square matrices
A
A
of order
3
3
.
D
If there is an invertible real
3
×
3
3\times3
matrix
A
A
such that
A
adj
(
A
)
=
4
I
A\operatorname{adj}(A)=4I
, then
det
(
adj
(
A
)
)
\det(\operatorname{adj}(A))
must be
4
4
.
