Question

In a square matrix of order 4, the element $a_{33}$ = 33. This square matrix cannot be skew hermitian.

• A. True
• B. False

Answer 1

The correct option is A

True

By definition of skew hermitian matrix we have, $aij=-\overline{aji}$

Lets see if its applied to a diagonal element what will be the result.

Let,

$a_{ii}$ = p + iq.

We have ,

$aij=-\overline{aji}$

i.e, p + iq = - (p – iq)

= - p + iq

$\Rightarrow$P = -p

2p = 0

P = 0

So the diagonal element of a skew hermitian matrix will always be purely imaginary or will be zero.

In this case its given that a diagonal element is equalto 33 which is a real number and violates the aforementioned condition. So the matrix cannot be skew hermitian and the given statement is correct.