Given A=21[1−331]
A2=41[1−331][1−331]
=41[1−3−2323−3+1]
A2=21[−1−33−1]
A3=41[−1−33−1][−1−33−1]
⇒A3=41[−400−4]=−[1001]
⇒A3=−I.....(1)
Now from equation (1),
A30=(−I)10=I.....(2)
Again from equation (1),
A25=(A3)8.A=(−I)8.A
⇒A25=A
⇒A25−A=0......(3)
On adding equations (2) and (3) we get,
A30+A25−A=I