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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 x 3 diagonal matrices, then
A
D
1
D
2
is a diagonal matrix
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B
D
1
+
D
2
is a diagonal matrix
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C
D
2
1
+
D
2
2
is a diagonal matrix
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D
1, 2, 3 are correct
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Solution
The correct option is
D
1, 2, 3 are correct
If
D
1
and
D
2
are diagonal matrix then
D
1
D
2
,
D
1
+
D
2
is also a diagonal matrix.
A
=
⎡
⎢ ⎢ ⎢
⎣
a
11
a
22
.
a
n
n
⎤
⎥ ⎥ ⎥
⎦
B
=
⎡
⎢ ⎢ ⎢
⎣
l
11
l
22
.
l
n
n
⎤
⎥ ⎥ ⎥
⎦
then,
A
B
=
⎡
⎢ ⎢ ⎢
⎣
a
11
l
11
a
22
l
22
.
a
n
n
l
n
n
⎤
⎥ ⎥ ⎥
⎦
A
+
B
=
⎡
⎢ ⎢ ⎢
⎣
a
11
+
l
11
a
22
+
l
22
.
a
n
n
+
l
n
n
⎤
⎥ ⎥ ⎥
⎦
A
2
=
⎡
⎢ ⎢ ⎢ ⎢
⎣
a
2
11
a
2
22
.
a
2
n
n
⎤
⎥ ⎥ ⎥ ⎥
⎦
∴
D
2
1
+
D
2
2
is also a diagonal matrix.
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