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UPSC NDA Math Model Paper 9
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© examsnet.com
Question : 32
Total: 120
Consider the following in respect of the matrix
A
=
[
−
2
2
2
−
2
]
1.
A
2
=
4
A
2.
A
3
=
2
4
A
Which of the above is/are correct?
Only 1
Only 2
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
Here,
A
=
[
−
2
2
2
−
2
]
A
2
=
A
×
A
=
[
−
2
2
2
−
2
]
[
−
2
2
2
−
2
]
=
[
−
8
8
8
−
8
]
=
−
4
[
−
2
2
2
−
2
]
=
−
4
A
Now,
A
3
=
A
2
×
A
=
[
−
8
8
8
−
8
]
[
−
2
2
2
−
2
]
=
[
−
32
32
32
−
32
]
=
16
[
−
2
2
2
−
2
]
=
16
A
=
2
4
A
Hence, option (2) is correct.
© examsnet.com
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