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Show that All the Diagonal Elements of a Skew Symmetric Matrix Are Zero. - CBSE (Commerce) Class 12 - Mathematics

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Question

Show that all the diagonal elements of a skew symmetric matrix are zero.

Solution

Let `A = [a_(ij)]` be a skewsymmetric matrix.

So,

`a_(ij) = -a_(ji)` for all i , j

`=> a_(ii) = -a_(ii)` for all value of i

`=> 2a_(ii) = 0 => a_(ii) = 0` for all value of i

`=> a_(11) = a_(22) = a_(33) = ... = a_"nn" = 0`

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Solution Show that All the Diagonal Elements of a Skew Symmetric Matrix Are Zero. Concept: Symmetric and Skew Symmetric Matrices.
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