Question

i) If A is a non-singular symmetric matrix, prove that adj. A is also symmetric.
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Answer 1

Answer:

f A is a symmetric matrix then A = A^t (where A^t denotes the transpose of the matrix A). we know that the adjugate preserves transposition. Therefore: 

adj(A) = adj(A^t) = [adj(A)]^t 

Therefore, since adj(A) = [adj(A)]^t then if A is symmetric then so is adj(A). 

Answer 2

Answer:

Let A be a symmetric matrix. Then, A  ^T  =A.

We know,

(adj A)^  T

=(adj A^  T  )

(adj A)^ T =adj A

adj A is a symmetric matrix.

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