This means that all the diagonal elements of a skew symmetric matrix are zero Rationalised 2023-24
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MATHEMATICS
For example, the matrix 
0
B
0
0
e
f
e
g
f
g




=
−



−
−


 is a skew symmetric matrix as B′= –B
Now, we are going to prove some results of symmetric and skew-symmetric
matrices Theorem 1 For any square matrix A with real number entries, A + A′ is a symmetric
matrix and A – A′ is a skew symmetric matrix Proof Let B = A + A′, then
B′ = (A + A′)′
= A′ + (A′)′ (as (A + B)′ = A′ + B′)
= A′ + A (as (A′)′ = A)
= A + A′ (as A + B = B + A)
= B
Therefore
B = A + A′ is a symmetric matrix
Now let
C = A – A′
C′ = (A – A′)′ = A′ – (A′)′     (Why