5.
Which of the following is true for the square matrix :
2.
1 O
A=0 2 11 ?
0 0 2
(B) A-1
(A) A-1 = }(A2 - 6A +121
A- = -(A2 - 6A - 121)
1-1-(A2 + 6A –121)
A-1 =-(A? + 6A – 121)
(C) A-1 =
(D)
Answers
A=[
2
3
−3
4
]
A
2
=[
2
3
−3
4
]×[
2
3
−3
4
]
=[
4−9
6+12
−6−12
−9+16
]
=[
−5
18
−18
7
]
6A=[
12
18
−18
24
]
A
2
−6A+17I
2
=[
−5−12+17
18−18
−18+18
7−24+17
]
=[
0
0
0
0
]=0 [Proved]
A
−1
=
17
1
[
4
3
−3
2
]
T
=
17
1
[
4
−3
3
2
]
det(A
−1
)=
17×17
8+9
=
17
1
A=[
2
3
−3
4
]
A
2
=[
2
3
−3
4
]×[
2
3
−3
4
]
=[
4−9
6+12
−6−12
−9+16
]
=[
−5
18
−18
7
]
6A=[
12
18
−18
24
]
A
2
−6A+17I
2
=[
−5−12+17
18−18
−18+18
7−24+17
]
=[
0
0
0
0
]=0 [Proved]
A
−1
=
17
1
[
4
3
−3
2
]
T
=
17
1
[
4
−3
3
2
]
det(A
−1
)=
17×17
8+9
=
17
1