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Byju's Answer
Standard XII
Mathematics
Skew Symmetric Matrix
Show that the...
Question
Show that the elements on the main diagonal of a skew-symmetric matrix are all zero.
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Solution
Let
A
=
[
a
i
j
]
be a skew-symmetric matrix. Then,
a
i
j
=
−
a
j
i
for all i, j.
a
i
i
=
−
a
i
i
for all values of i.
2
a
i
i
=
0
a
i
i
=
0
for all values of i.
⟹
a
11
=
a
22
=
a
33
=
.
.
.
=
a
n
n
=
0
.
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