Find the determinant
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the elements of the matrix.
The given matrix is a $2 \times 2$ matrix:
$$A = \begin{bmatrix} -3 & -3 \\ 4 & 1 \end{bmatrix}$$
Step 2: Calculate the determinant of the $2 \times 2$ matrix.
The formula for the determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is $ad - bc$.
Applying this formula to matrix $A$:
$$\det(A) = (-3)(1) - (-3)(4)$$
Step 3: Perform the multiplication.
$$\det(A) = -3 - (-12)$$
Step 4: Simplify the expression.
$$\det(A) = -3 + 12$$
$$\det(A) = 9$$
The determinant of the matrix is $\boxed{9}$.
