a) pt a=1 si b=0, I 2∈M
b) det M= a²-b²=(a-b)(a+b)=1=1*1=(-1)*(-1)
a-b=1
a+b=1⇒2a=2⇒a=1 si b=o avem I2
a-b=-1
a=b=-1⇒2a=-2⇒a=-1sib=0 avem matricea -I2
I2 si-I2 , exact 2 matrici
c) detM=a²-b²=(a-b)(a+b)=6=2*3=3*2=(-2)*(-3) =(-3)*(-2)=6*1=1*6= (-6)*(-1) =(-1)*(-6)
calculand fiecare varianta (vezi atasament)⇒a∉Z,deci nu exista a,b∈Z a.î. Det M=6, C.C.T.D.
as simple as that!
