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Matrix is such that
MATHEMATICS · Single correct · CBSE · Mathematics · Matrices · Matrices
Problem
Matrix
A
A
A
is such that
A
2
=
2
A
−
I
A^2 = 2A - I
A
2
=
2
A
−
I
, where
I
I
I
is the identity matrix. Then, for
n
≥
2
n \geq 2
n
≥
2
,
A
n
A^n
A
n
is equal to (1)
n
A
−
(
n
−
1
)
I
nA - (n-1)I
n
A
−
(
n
−
1
)
I
(2)
n
A
−
I
nA - I
n
A
−
I
(3)
2
n
−
1
A
−
(
n
−
1
)
I
2^{n-1}A - (n-1)I
2
n
−
1
A
−
(
n
−
1
)
I
(4)
2
n
−
1
A
−
I
2^{n-1}A - I
2
n
−
1
A
−
I
Related theory
Mathematical Logic
Matrices
Matrix operations
Properties of matrix operations
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