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AP EAMCET Engineering 17 Sep 2020 Shift 2 Paper
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© examsnet.com
Question : 10
Total: 160
Let
M
and
N
be two matrices over
R
of order
2
. Then
M
N
=
N
M
if _______
One of M and A is a diagonal matrix
Both M and N are diagonal matrices
Both M and N are invertible matrices
None of these options are true in general
Validate
Solution:
Let
M
=
(
a
b
c
d
)
,
N
=
(
p
q
r
s
)
Then,
M
N
=
(
a
p
+
b
r
a
q
+
b
s
p
c
+
d
r
c
q
+
d
s
)
and
N
M
=
(
a
p
+
q
c
p
b
+
q
d
a
r
+
c
s
b
r
+
d
s
)
Clearly,
M
N
=
N
M
When,
b
r
=
0
,
q
c
=
0
p
c
=
0
,
d
r
=
0
.
.
.
or, If
b
=
c
=
q
=
r
=
0
i.e., both
M
and
N
must be diagonal matrices.
© examsnet.com
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