The square matrix $A =[a_{ij}]$ given by

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

The square matrix $A =[a_{ij}]$ given by $a_{ij} = (i-j)^3$, is a

Options:

symmetric matrix

skew-symmetric matrix

diagonal matrix

hermitian matrix

Correct Answer:

skew-symmetric matrix

Explanation:

We have,

$a_{ij} = (i-j)^3⇒a_{ij} =(j-i)^3=-(i-j)^3=-a_{ij}$ for all i, j

∴ A is a skew-symmetric matrix.