Step 1: Identify the elements of the matrix. The given matrix is a 2 × 2 matrix: A = −3 & −3 4 & 1 Step 2: Calculate the determinant of the 2 × 2 matrix. The formula for the determinant of a 2 × 2 matrix a & b c & d 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 9.

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Find the determinant

April 9, 2026Mathematics

ScanSolve AI Answer

Answer

9

Step-by-step solution

4 steps

Identify the elements of the matrix.
The given matrix is a $2 \times 2$ matrix:
$A = \begin{bmatrix} -3 & -3 \\ 4 & 1 \end{bmatrix}$
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 $A$ :
$\det(A) = (-3)(1) - (-3)(4)$
Perform the multiplication.
$\det(A) = -3 - (-12)$
Simplify the expression.
$\det(A) = -3 + 12$ $\det(A) = 9$
The determinant of the matrix is 9.