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

ConceptSymmetric and Skew Symmetric Matrices

#### 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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