Define a symmetric matrix. Prove that A + AT is a symmetric matrix where AT is the transpose of A.

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Define a symmetric matrix. Prove that A + A^T is a symmetric matrix where A^T is the transpose of A.

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A square matrix A is said to be a symmetric if A^T = A.

Let, B = A + A^T.

Now,

B^T = (A + A^T)^T

= A^T + (A^T)^T

= A^T + A [ Since (A^T)^T = A]

= B.

So B is symmetric.

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