(A + A’) is a symmetric matrix.

On adding them we get,

Explanation: Now to show that the matrix obtained i.e. (A + A’) is symmetric we need to calculate its transpose and prove that the matrix (A + A’) and its transpose are equal. This means that (A + A’) = (A + A’)’.

. → eqⁿ 2

So, from equation 1 & 2 we get,

(A + A’) = (A + A’)’, hence we can say that (A + A’) is a symmetric matrix.

Ans. Hence proved.