1.
D=∣104+2107+3108+8109+9102+8103−4103−5108+b106+a∣D = \begin{vmatrix} 10^4+2 & 10^7+3 & 10^8+8 \\ 10^9+9 & 10^2+8 & 10^3-4 \\ 10^3-5 & 10^8+b & 10^6+a \end{vmatrix} where a,ba, b, both ∈{1,2,3,4,5,6,7,8,9}\in \{1,2,3,4,5,6,7,8,9\}.

Number of ordered pairs (a,b)(a, b) such that D=2n+1,n∈ZD = 2n+1, n \in \mathbb{Z} is
Matrices and Determinants - Hard - Question