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

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3 and 4 .Determinants and Matrices

easy

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

D

Skew symmetric matrix

Solution

(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.

Standard 12

Mathematics

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