Algebra

Matrices & Determinants

Medium

common

If $A = [a_{ij}]$ is skew symmetric matrix of order 'n', then

$a_{ij} = \frac{1}{a_{ji}}$ for all $i, j$

$a_{ij} = 0$ for $i = j$

$a_{ij} = 0$ for all $i, j$

$a_{ij} \neq 0$ for $i = j$

✅ Correct Option: 2

A matrix $A$ is skew-symmetric if:

$A^T = -A$

For any element $a_{ij}$ in the matrix:

$a_{ij} = -a_{ji}$

For diagonal elements where $i = j$ :

$a_{ii} = -a_{ii}$

$a_{ii} + a_{ii} = 0$

$2a_{ii} = 0$

$a_{ii} = 0$

All diagonal elements must be zero.

Option 1: $a_{ij} = \frac{1}{a_{ji}}$

This is not a property of skew-symmetric matrices.

Option 2: $a_{ij} = 0$ for $i = j$

This is correct. All diagonal elements (where $i = j$ ) must be zero.

Option 3: $a_{ij} = 0$ for all $i, j$

This is incorrect. Only diagonal elements are zero. Off-diagonal elements can be non-zero.

Option 4: $a_{ij} \neq 0$ for $i = j$

This is incorrect. Diagonal elements must be zero.

Therefore, the answer is Option 2.

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If A=[aij]A = [a_{ij}]A=[aij​] is skew symmetric matrix of order 'n', then

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = [a_{ij}]$ is skew symmetric matrix of order 'n', then