Question

How to prove AA' and A + A' are symmetric matrices. Take A as any matrix. Please don't post any irrelevant answers​

Answer 1

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FORMULA TO BE IMPLEMENTED

1.

A square Matrix B is said to Symmetric Matrix if

$( B ' ) ' = B$

Where B ' = Transpose of B

2. Transpose of the transpose of a matrix is the matrix itself

3.

$( AB)' = B ' A'$

4.

$( A+ B)' = A' + B'$

CALCULATION

1.

Let

$B = AA'$

Then

$\: B ' = ( AA' ) ' = ( A') ' A' = A A' = B$

So AA' is symmetric matrix

2. Let

$E = A + A'$

Then

$E ' = ( A + A') '= A' +(A') '= A' + A = A + A' = E$

So A+ A' is a symmetric matrix

Answer 2

Answer:

A + Á IS THE SYMMETRIC MATRIX..

Step-by-step explanation:

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