Question

For any square matrix A, show that AA' is symmetric.

Answer 1

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

Any matrix is said to be symmetric if :

• The matrix must be square matrix

• The transpose of the matrix must be equal to itself.

Now, The matrix A is given to be square.

$\text{So, }AA^T\text{ is also square matrix}\\\text{Therefore, we only need to show that that : }(AA^T)^T=AA^T$

$\text{Proof : }(AA^T)^T=(A^T)^T\thinspace A^T\text{ By using reversible law}\\\\=A\thinspace A^T\text{ (Because }(A^T)^T=A)\\\\=A\thinspace A^T\\\\\implies AA^T\text{ is symmetric}$

Hence Proved.

Answer 2

Answer: The matrix must be square matrix

The transpose of the matrix must be equal to itself.

Now, The matrix A is given to be square.

Step-by-step explanation: