Question 12 - Week 7 Practice | Prasnya
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Week 7
Field
IITM-DS
Exam
Quiz 2
Subject
Mathematics 2
Week
Week 7
Question 12 of 43
Practice question
00:00
Est. 3 min
Marks
+4.00
0.00
Question
Let
A
=
[
2
−
3
4
1
]
A=\begin{bmatrix}2&-3\\4&1\end{bmatrix}
. Choose all the correct options.
Multiple correct
Medium Difficulty
16 March 2025
A
If
A
A
is equivalent to a matrix
B
B
, then they have the same rank, trace, and determinant.
B
B
∈
M
2
×
2
(
R
)
B\in M_{2\times2}(\mathbb{R})
is a matrix with the same rank, trace, and determinant as
A
A
. Then
A
A
and
B
B
are similar.
C
B
∈
M
2
×
2
(
R
)
B\in M_{2\times2}(\mathbb{R})
is a matrix such that
A
=
[
0
−
1
5
0
]
B
A=\begin{bmatrix}0&-1\\5&0\end{bmatrix}B
. Then
A
A
and
B
B
are equivalent.
D
A
A
is equivalent to any
2
×
2
2\times2
orthogonal matrix.
