Matrix Determinant Calculation
<p>The provided photo seems to show the determinant of a 3x3 matrix being calculated. However, the step-by-step calculation is not fully visible, and there's some text in another language at the bottom. With the visible content, I will assume the goal is to calculate the determinant of a matrix displayed at the top right corner of the image.</p>
<p>Let the matrix A be:</p>
\[
A = \begin{bmatrix}
-3 & 1 & 5 \\
1 & -3 & -5 \\
1 & 3 & 5 \\
\end{bmatrix}
\]
<p>To find the determinant of matrix A (denoted as det(A) or |A|), we can use the following formula for a 3x3 matrix:</p>
<p>det(A) = a_{11}(a_{22}a_{33} - a_{23}a_{32}) - a_{12}(a_{21}a_{33} - a_{23}a_{31}) + a_{13}(a_{21}a_{32} - a_{22}a_{31})</p>
<p>Substituting the values from matrix A, we get:</p>
\[
\begin{align*}
\text{det}(A) &= (-3)((-3)(5) - (-5)(3)) - (1)((1)(5) - (3)(-5)) + (5)((1)(3) - (-3)(1)) \\
&= (-3)((-15) - (-15)) - (1)((5) - (-15)) + (5)((3) - (-3)) \\
&= (-3)(0) - (1)(20) + (5)(6) \\
&= 0 - 20 + 30 \\
&= 10
\end{align*}
\]
<p>Therefore, the determinant of matrix A is 10.</p>
