Question

how do I define symmetry

Answer 1

A proper proportion between parts, possession of corresponding parts that are exactly alike

It is actually the same as invariance: the property that something does not change under a set of transformations.

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, matrix A is symmetric if A=A(TRANSPOSE)
FOR EXAMPLE :
                                  C1  C2  C3
VALUE IN MARTIX A    1    7    3    ---- >ROW A     
                                    7    4    5   ---- >ROW B
                                    3    5    6   ---- >ROW C
                                  
U CAN C ROW A IS SIMILAR TO COLUMN (C1)
U CAN C ROW B IS SIMILAR TO COLUMN (C2)
U CAN C ROW C IS SIMILAR TO COLUMN (C3)
 
                                  

Answer 2

Symmetry is an alternative to a matter's size,shape etc. given in a same proportion .