Denote by $I$ the $2 \times 2$ identity matrix, and let

$D =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $0$ $-17$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $1$ $0$

Denote by $A( -17 )$ the set of matrices of the form $sI + tD$, where $s, t$ are rational numbers. It is a fact that $A( -17 )$ is a commutative ring with a multiplicative identity under matrix addition and multiplication.

(a) Is $A( -17 )$ a field?
Yes
No

(b) If $A( -17 )$ is a field, enter an ordered pair of rational numbers $( s, t )$ such that $sI + tD$ is the multiplicative inverse of $I - D$. If $A( -17 )$ is not a field, enter an ordered pair of non-zero rational numbers $( s, t )$ such that $sI + tD$ is a zero-divisor.
$I +$ $D$

Hint: