$$ \begin{vmatrix}\text{ 2 }-5\\ 0\text{  }7\end{vmatrix} $$$$ ^2 $$

The given matrix is:

\[
\begin{vmatrix}
2 & -5 \\
0 & 7
\end{vmatrix}
\]

First, we calculate the determinant of the matrix. For a 2x2 matrix of the form:

\[
\begin{vmatrix}
a & b \\
c & d
\end{vmatrix}
\]

the determinant is calculated as:

\[
\text{det} = ad - bc
\]

Here, $ a = 2 $, $ b = -5 $, $ c = 0 $, and $ d = 7 $. Thus:

\[
\text{det} = (2 \times 7) - (0 \times -5) = 14
\]

Now, the problem asks for the square of the determinant:

\[
\text{det}^2 = 14^2 = 196
\]

Therefore, the answer is:

\[
196
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you find the determinant of a 3x3 matrix?
2. Can you explain how to invert a 2x2 matrix?
3. What are the properties of matrix determinants?
4. How does the determinant help in solving systems of linear equations?
5. What happens if the determinant of a matrix is zero?

### Tip:
When the determinant of a matrix is zero, the matrix is called "singular" and does not have an inverse.

The determinant of the matrix $$ \begin{vmatrix}2 & -5\\ 0 & 7\end{vmatrix} $$ squared.

Learn how to calculate the determinant of a 2x2 matrix and square the result with a step-by-step example. This solution covers the formula for finding the determinant and explains the calculation process in detail. Suitable for students in Grades 9-12.

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