||'''Book'''|| Linear Algebra ||
 ||'''Author'''|| Gilbert Strang ||
 ||'''Edition'''||  ||

/* code_begins */

{{{
a = var('a')
b=var('b')
c=var('c')
d=var('d')
A = matrix([[a,b],[c,d]])
print A,
print " = A"
print "------------------"
I = matrix([[1,0],[0,1]])
print I,
print " = I"
print "------------------"
#C = matrix([[1,0.5],[-0.5,-1]])
B = A*A
print B,
print " but given that, b = 1/2, substituting the given value we get "
#A = matrix([[a,0.5],[c,d]])
B = A*A
print B
print " by solving equations with I, we get a=-d and c=(1-a^2)/0.5"
print "================================================="
print " similarly for A^2 = A "
print " by solving equations for A^2 = A, we get either a=d or a=-d and c=(a-a^2)/0.5"
print "================================================="
}}}

/* code_ends */

 * '''Solution by''': 
   * Ch.Sandeep, student, GITAM University
   * V.Vishnu Sarma, student, GITAM University