Question

In a skew-symmetric matrix, the diagonal elements are all

• A. one
• B. zero
• C. different from each other
• D. non-zero

Answer 1

The correct option is B zero

a matrix is called skew symetric if

$[A^T=-A]$

$\Rightarrow A_{ij}=-A_{ij}$

so, for $i=j$ (i.e for diagonal elements )

$\Rightarrow A_{ii}=-A_{ii}$

$\Rightarrow A_{ii}=-A_{ii}$

$\Rightarrow 2A_{ii}=0$

$\Rightarrow A_{ii}=0$

$\Rightarrow A_{11}=A_{22}=A_{33}.........=0$

$\therefore$ in skew symmetric matrix diagonal elements are zero.