||'''Book'''|| Advanced Engineering Mathematics ||
 ||'''Author'''|| Erwin Kreyszig ||
 ||'''Edition'''|| 8th Edition ||

/* code_begins */

{{{
a , b = var('a, b')

A = matrix([[a,b],[-b,a]])

print A


A.characteristic_polynomial()

A.eigenvalues()

#moduli of the eigenvalues = sqrt(a^2 + b^2)

# b = 0 => the matrix is symmetric 

# a = 0 => the matrix is not skew-symmetric

# sqrt(a^2 + b^2) = 1 => the matrix is orthogonal



}}}

/* code_ends */

 * '''Solution by''': 
  * ganesh, developer, space
  * bhanukiran, student, technical university of Delft
  * saransh, student, sobhit university
  * ujwala, lecturer, aurangabad