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Byju's Answer
Standard XII
Mathematics
Multiplication of Matrices
Compute A2 ...
Question
Compute
A
2
−
4
A
−
5
Where A =
⎡
⎢
⎣
1
2
2
2
1
1
2
2
1
⎤
⎥
⎦
and I is a unit matrix
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Solution
A
2
=
⎡
⎢
⎣
1
2
2
2
1
1
2
2
1
⎤
⎥
⎦
∴
A
2
−
4
A
−
5
I
=
⎡
⎢
⎣
1
2
2
2
1
1
2
2
1
⎤
⎥
⎦
-
⎡
⎢
⎣
4
8
8
8
4
8
8
8
4
⎤
⎥
⎦
-
⎡
⎢
⎣
5
0
0
0
5
0
0
0
5
⎤
⎥
⎦
=
⎡
⎢
⎣
0
−
2
−
2
−
2
0
−
2
−
2
−
2
0
⎤
⎥
⎦
= -2
⎡
⎢
⎣
0
1
1
1
0
1
1
1
0
⎤
⎥
⎦
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Similar questions
Q.
If
A
=
[
1
−
1
2
3
]
and
I
is the units matrix of order
2
, then
A
2
−
4
A
+
5
equals to?
Q.
If
A
=
⎛
⎜
⎝
1
2
2
2
1
2
2
2
1
⎞
⎟
⎠
If
A
2
−
4
A
=
p
I
where
I
and
O
are the unit matrix and the null matrix of order
3
respectively. Find the value of
p
Q.
If matrix
A
=
[
1
−
1
2
3
]
, then prove that
A
2
−
4
A
+
5
I
=
0
, where
I
is a unitary matrix.
Q.
A
skew-symmetric matrix
A
satisfies the relation
A
2
+
I
=
0
, where
I
is a unit matrix then
A
is
Q.
Show that the matrix
A
=
[
2
3
1
2
]
satisfies the equation
A
2
−
4
A
+
I
=
0
, where
I
is
2
×
2
identity matrix and
0
is
2
×
2
zero matrix. Using this equation,find
A
−
1
.
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