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CBSE Class 12 · 2017 · MatricesLong Answer

Show that all the diagonal elements of a skew symmetric matrix are zero.

Answer: Proved

Solution

Let

A = [a_{ij}]

be skew-symmetric, so

A^{'} = - A

, i.e.

a_{ij} = - a_{j i}

for all

i, j

.
For a diagonal element take

i = j

:

a_{ii} = - a_{ii} \Rightarrow 2 a_{ii} = 0 \Rightarrow a_{ii} = 0.

Thus every diagonal entry of a skew-symmetric matrix is zero. Proved.

CBSE Class 12 Board · 2017 · Subjective

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