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Question

Let a denote the element of the ith row and jth column in a 3×3 matrix and let aij=aji for every i and j then this matrix is an -

A
Orthogonal matrix
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B
singular matrix
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C
matrix whose principal diagonal elements are all zero
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D
skew-symmetric matrix
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Solution

The correct option is B skew-symmetric matrix
If aij is the element of ith row and jth column and aij=aji
then lets assume
A=a11a12a13a21a22a23a31a32a33

Where, aij=aji

a11=a11a11=0, similarly a22=a33=0

and a21=a12,a31=a13,a32=a23

Putting the values
A=0a12a13a120a23a13a230

AT=0a12a13a120a23a13a230
and
A=0a12a13a120a23a13a230
thus
AT=A

The matrix is a skew-symmetric matrix.

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