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

/* code_begins */
(((
A = matrix([[-3,1,5],[1,0,-2],[5,-2,4]])
print A
 print A.transpose()
print "Is symmetric?", A.is_symmetric()
print "Is skew_symmetric?", A.is_skew_symmetric()
if ( A.is_invertible()==true):
    if(A.transpose()==A.inverse()):
        print "matrix is orthogonal"
    else:
        print "matrix is not orthogonal"
else:
    print"matrix is not orhtogonal"


B = matrix ([[0,9,-12],[-9,0,20],[12,-20,0]])
print B



print B.transpose()
print "Is symmetric?",B.is_symmetric()
print "Is skew_symmetric?", B.is_skew_symmetric()

if ( B.is_invertible()==true):
    if(B.transpose()==B.inverse()):
        print "matrix is orthogonal"
    else:
        print "matrix is not orthogonal"
else:
    print"matrix is not orhtogonal"

C = matrix ([[2/3,1/3,2/3],[-2/3,2/3,1/3],[1/3,2/3,-2/3]])
print C

print C.transpose()
print "Is symmetric?",C.is_symmetric()
print "Is skew_symmetric?", C.is_skew_symmetric()
if ( C.is_invertible()==true):
    if(C.transpose()==C.inverse()):
        print "matrix is orthogonal"
    else:
        print "matrix is not orthogonal"
else:
    print"matrix is not orhtogonal"

    )))

/* code_ends */

 * '''Solution by''': 
   * srinivas vinay, student, vardhaman college of engineering
   * <Your Name>, <Profession>, <Organization>