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Question
Mathematics
If A is a square matrix such that A2=A, then (1-A)3+A is equal to
Q. If A is a square matrix such that
A
2
=
A
, then
(
1
−
A
)
3
+
A
is equal to
6576
208
Matrices
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A
A
8%
B
I
−
A
38%
C
I
32%
D
3
A
22%
Solution:
A is a square matrix such that
A
2
= A
Now
(
I
−
A
)
3
+
A
=
(
I
−
A
)
2
(
I
−
A
)
+
A
=
(
I
2
−
2
A
I
+
A
2
)
(
I
−
A
)
+
A
=
(
I
−
2
A
+
A
)
(
I
−
A
)
+
A
(
∵
A
2
=
A
)
=
(
I
−
A
)
(
I
=
A
)
+
A
=
(
I
2
−
2
A
I
+
A
2
)
+
A
=
(
I
−
2
A
+
A
)
+
A
(
∵
A
2
=
A
)
=
I
−
A
+
A
= 1
∴
(
I
−
A
)
3
+
A
=
I