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AP EAPCET 25-Aug-2021 Shift 1 Paper
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© examsnet.com
Question : 2
Total: 160
Let
A
be the set of all
3
×
3
scalar matrices with real entries. If
f
:
A
→
R
is defined by
f
(
m
)
=
d
e
t
(
m
)
∀
m
∈
A
, then
′
f
' is ______
One - one but not onto
Onto but not one - one
Bijective
Neither one
−
one nor onto
Validate
Solution:
A be a scalar matrix
A
=
[
m
0
0
0
m
0
0
0
m
]
|
A
|
=
m
3
⇒
f
(
m
)
=
m
3
∴
f
(
m
)
is injective.
Range of
f
(
m
)
=
R
=
codomain
∴
f
(
m
)
is surjective.
Hence,
f
(
m
)
is bijective.
© examsnet.com
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