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COMEDK Exam 2014 Solved Paper
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© examsiri.com
Question :
160 of 180
Marks:
+1
,
-0
A
and
B
are two matrices such that
A
B
=
B
,
B
A
=
A
, then
A
2
+
B
2
=
2
A
B
2
B
A
A
+
B
A
B
Validate
Solution:
Given,
A
B
=
B
Multiply by
A
on both sides
A
B
A
=
B
A
...........(i)
Also,
B
A
=
A
Multiply by
B
on both sides
B
A
B
=
A
B
...........(ii)
Adding Eqs. (i) and (ii), we get
A
B
A
+
B
A
B
=
B
A
+
A
B
⇒
A
(
B
A
)
+
B
(
A
B
)
=
B
A
+
A
B
⇒
A
A
+
B
B
=
A
+
B
⇒
A
2
+
B
2
=
A
+
B
© examsiri.com
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