A2=⎡⎢⎣10002030−1⎤⎥⎦⎡⎢⎣10002030−1⎤⎥⎦=⎡⎢⎣100040001⎤⎥⎦
A3=⎡⎢⎣100040001⎤⎥⎦⎡⎢⎣10002030−1⎤⎥⎦=⎡⎢⎣10008030−1⎤⎥⎦
A4=⎡⎢⎣100040001⎤⎥⎦⎡⎢⎣100040001⎤⎥⎦=⎡⎢⎣1000160001⎤⎥⎦
⋮ ⋮ ⋮
A19=⎡⎢⎣1000219030−1⎤⎥⎦,A20=⎡⎢⎣10002200001⎤⎥⎦
L. H. S
=A20+αA19+βA=⎡⎢⎣1+α+β000220+α219+2β03α+3β01−α−β⎤⎥⎦
R.H.S
=⎡⎢⎣100040001⎤⎥⎦⇒α+β=0
and 220+α219+2β=4
⇒220+α(219−2)=4
⇒α=4−220219−2=−2⇒β=2
∴β−α=4