Question 18 - Week 1 Practice | Prasnya
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Week 1
Question 18
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Est. 3 min
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Choose the correct option(s) from the following:
Multiple correct
Medium Difficulty
27 October 2024
A
Let
A
,
B
∈
M
n
×
n
(
R
)
A,B\in M_{n\times n}(\mathbb{R})
such that
A
B
=
0
AB=0
. Then at least one of the matrices
A
A
or
B
B
must have determinant
0
0
.
B
If
A
−
α
I
=
0
A-\alpha I=0
where
A
∈
M
n
×
n
(
R
)
A\in M_{n\times n}(\mathbb{R})
,
I
I
is the identity matrix of order
n
n
,
α
∈
R
\alpha\in\mathbb{R}
and
n
n
is even, then determinant of
A
A
is always positive.
C
A matrix with all diagonal entries as zero will always have determinant zero.
D
For a square matrix
A
A
, if the system of linear equations
A
x
=
0
Ax=0
has a unique solution, then determinant of
A
A
is non-zero.
