If the matrix A=10002030−1satisfies the equation A20+αA19+βA=100040001for some real numbers αand βthen β−α is equal to ___

A2=10002030−110002030−1=100040001⇒A4=100040001100040001=1000160001similarly  A19=1000219030−1 and A20=10002200001∴A20+αA19+βA=1+α+β000220+α219+2β03α+3β01−α−β=100040001By equating the corresponding elements ⇒α+β=0220+α219+2β=4 it implies ⇒α=−2⇒β−α=4