If the matrix A=⎡⎢⎣10002030−1⎤⎥⎦ satisfies the equation A20+αA19+βA=A=⎡⎢⎣100040001⎤⎥⎦ for some real numbers α andβ, then β−α is equal to

If the matrix A=⎡⎢⎣10002030−1⎤⎥⎦ satisfies the equation

1.	If the matrix A=⎡⎢⎣10002030−1⎤⎥⎦ satisfies the equation A20+αA19+βA=A=⎡⎢⎣100040001⎤⎥⎦ for some real numbers α andβ, then β−α is equal to
Answer» If the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 2 & 0 3 & 0 & - 1 \end{matrix} ⎤ ⎥ ⎦$ satisfies the equation $A^{20} + α A^{19} + β A = A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 4 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦$ for some real numbers $α$ and $β$ , then $β - α$ is equal to