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Byju's Answer
Standard XII
Mathematics
Transpose of a Matrix
If D1 and ...
Question
If
D
1
and
D
2
are two
3
×
3
diagonal matrices, then
A
D
1
D
2
is diagonal matrix
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B
D
1
D
2
=
D
2
D
1
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C
D
2
1
+
D
2
2
is a diagonal matrix
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D
none of these
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Solution
The correct options are
A
D
2
1
+
D
2
2
is a diagonal matrix
C
D
1
D
2
is diagonal matrix
D
D
1
D
2
=
D
2
D
1
Let
D
1
=
⎡
⎢
⎣
a
0
0
0
b
0
0
0
c
⎤
⎥
⎦
,
D
2
=
⎡
⎢
⎣
x
0
0
0
y
0
0
0
z
⎤
⎥
⎦
Then
D
1
D
2
=
⎡
⎢
⎣
a
0
0
0
b
0
0
0
c
⎤
⎥
⎦
⎡
⎢
⎣
x
0
0
0
y
0
0
0
z
⎤
⎥
⎦
=
⎡
⎢
⎣
a
x
0
0
0
b
y
0
0
0
c
z
⎤
⎥
⎦
D
2
D
1
=
⎡
⎢
⎣
x
0
0
0
y
0
0
0
z
⎤
⎥
⎦
⎡
⎢
⎣
a
0
0
0
b
0
0
0
c
⎤
⎥
⎦
=
⎡
⎢
⎣
x
a
0
0
0
y
b
0
0
0
z
c
⎤
⎥
⎦
As
a
x
=
x
a
,
b
y
=
y
b
,
c
z
=
z
c
D
1
D
2
=
D
2
D
1
D
1
2
+
D
2
2
=
⎡
⎢
⎣
a
0
0
0
b
0
0
0
c
⎤
⎥
⎦
⎡
⎢
⎣
a
0
0
0
b
0
0
0
c
⎤
⎥
⎦
+
⎡
⎢
⎣
x
0
0
0
y
0
0
0
z
⎤
⎥
⎦
⎡
⎢
⎣
x
0
0
0
y
0
0
0
z
⎤
⎥
⎦
=
⎡
⎢
⎣
a
2
0
0
0
b
2
0
0
0
c
2
⎤
⎥
⎦
+
⎡
⎢
⎣
x
2
0
0
0
y
2
0
0
0
z
2
⎤
⎥
⎦
=
⎡
⎢ ⎢ ⎢
⎣
a
2
+
x
2
0
0
0
b
2
+
y
2
0
0
0
c
2
+
z
2
⎤
⎥ ⎥ ⎥
⎦
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