The value of the determinant is

Question

The value of the determinant  is

Quizplus · Accepted Answer

The determinant involves a matrix with entries in base 16. First, we need to convert these entries to base 10:
\begin{align*}
\begin{vmatrix}
1 & e & a & b \
b & 8 & b & e \
b & 8 & d & b \
6 & 5 & 73 & 26
\end{vmatrix} &= \begin{vmatrix}
1 & 14 & 10 & 11 \
11 & 8 & 11 & 14 \
11 & 8 & 13 & 11 \
6 & 5 & 115 & 38
\end{vmatrix} \
&= \begin{vmatrix}
1 & 14 & 10 & 11 \
0 & 14\pmod 9 & 5\pmod 9 & 9\pmod 9 \
0 & 14\pmod 9 & 3\pmod 9 & 0\pmod 9 \
0 & 3\pmod 9 & 53\pmod 9 & 5\pmod 9
\end{vmatrix} \
&= \begin{vmatrix}
14\pmod 9 & 5\pmod 9 & 9\pmod 9 \
14\pmod 9 & 3\pmod 9 & 0\pmod 9 \
3\pmod 9 & 53\pmod 9 & 5\pmod 9
\end{vmatrix} \
&= \begin{vmatrix}
5\pmod 9 & 9\pmod 9 \
53\pmod 9 & 5\pmod 9
\end{vmatrix} \
&= (5\cdot 5 - 53\cdot 9) \pmod 9 \
&= (-472) \pmod 9 \
&= -4
\end{align*}
Therefore, the answer is $\boxed{	extbf{(D)}}$.

The Value of the Determinant Is