Problem

Evaluate the determinant of $\left|\begin{array}{cc}9 & 0 \\ 8 & -8\end{array}\right|$.
\[
\left|\begin{array}{cc}
9 & 0 \\
8 & -8
\end{array}\right|=
\]
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Answer

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Answer

Final Answer: The determinant of the matrix is \(\boxed{-72}\)

Steps

Step 1 :Given the matrix $\left|\begin{array}{cc}9 & 0 \ 8 & -8\end{array}\right|$

Step 2 :The determinant of a 2x2 matrix $\left|\begin{array}{cc}a & b \ c & d\end{array}\right|$ is calculated as \(ad - bc\)

Step 3 :Substitute a = 9, b = 0, c = 8, d = -8 into the formula

Step 4 :The determinant is calculated as \( (9*-8) - (0*8) \)

Step 5 :Simplify to get the determinant as -72

Step 6 :Final Answer: The determinant of the matrix is \(\boxed{-72}\)

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