If A is a square matrix for which a_ ij = i^2 - j^2 , then A is - Vidyadip

MCQ

If $A$ is a square matrix for which ${a_{ij}} = {i^2} - {j^2}$, then $A$ is

A
Zero matrix
B
Unit matrix
C
Symmetric matrix
✓
Skew symmetric matrix

✓

Answer

Correct option: D.

Skew symmetric matrix

d
(d) ${a_{ji}} = {i^2} - {j^2}$ is a square matrix.

For a skew symmetric matrix ${a_{ji}} = -{a_{ji}}$

$\Rightarrow$ ${a_{ij}} = {i^2} - {j^2}$ and ${a_{ji}} = {j^2} - {i^2}$

$\Rightarrow$ ${a_{ij}} + {a_{ji}} = 0$

$\Rightarrow \,{a_{ij}} = - {a_{ji}}$

Hence, $ {a_{ji}}$ is a skew symmetric matrix.

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