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AP EAPCET 08-Jul-2022 Shift 2 Paper
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© examsnet.com
Question : 3
Total: 160
If
A
and
B
are nxn square matrices such that
(
2
A
+
B
)
2
+
(
A
−
3
B
)
2
=
5
A
2
−
2
A
B
+
10
B
2
then,
A
B
A
B
=
1
2
[
(
A
−
B
)
2
+
(
A
+
B
)
2
]
4
A
B
1
2
[
(
A
+
B
)
2
−
(
A
−
B
)
2
]
A
2
B
2
Validate
Solution:
Given,
(
2
A
+
B
)
2
+
(
A
−
3
B
)
2
=
5
A
2
−
2
AB
+
10
B
2
⇒
4
A
2
+
B
2
+
2
AB
+
2
BA
+
A
2
+
9
B
2
−
3
AB
−
3
BA
−
5
A
2
+
2
AB
−
10
B
2
=
0
⇒
AB
−
BA
=
0
⇒
AB
=
BA
than,
ABAB
=
(
AB
)
(
AB
)
=
(
AA
)
(
BA
)
=
A
2
B
2
© examsnet.com
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