Determinant of 3×3 Matrix Problems with Answers

Use the following ten (10) practice problems to get better at solving the Determinant of a 3×3 Matrix. With practice, you’ll get better at it until it becomes second nature.

You may use these problems for independent practice, homework, cooperative learning, and more!

Problem 1: Find the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} 7 & -4 & 2 \\ 3 & 1 & -5 \\ 2 & 2 & -5 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {7,-4,2},{3,1,-5},{2,2,5} } is 23

Problem 2: Find the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} 1 & -6 & -7 \\ 1 & -4 & 7 \\ -1 & -3 & -6 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {1,-6,-7},{1,-4,7},{-1,-3,-6} } is 100

Problem 3: Find the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} -1 & -1 & -1 \\ 4 & 5 & -3 \\ -1 & -6 & 3 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {-1,-1,-1},{4,5,-3},{-1,-6,3} } is 31

Problem 4: Calculate the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} 7 & 5 & 7 \\ 6 & -5 & -5 \\ 6 & 2 & 3 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {7,5,7},{6,-5,-5},{6,2,3} } is 19

Problem 5: Calculate the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} 4 & -6 & 4 \\ -4 & -7 & -5 \\ 2 & 7 & 3 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {4,-6,4},{-4,-7,-5},{2,7,3} } is -12

Problem 6: Calculate the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} -1 & -3 & 4 \\ -1 & 2 & 6 \\ -3 & -7 & 2 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {-1,-3,4},{-1,2,6},{-3,-7,2} } is 54

Problem 7: Determine the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} 2 & 7 & 5 \\ 1 & 2 & 5 \\ 0 & 0 & -4 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {2,7,5},{1,2,5},{0,0,-4} } is 12

Problem 8: Determine the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} 1 & -2 & 2 \\ -5 & -1 & 5 \\ 4 & -1 & 0 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {1,-2,2},{-5,-1,5},{4,-1,0} } is -17

Problem 9: Compute the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} -5 & 2 & -3 \\ -2 & -1 & -5 \\ 5 & -5 & -3 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {-5,2,-3},{-2,-1,-5},{5,-5,-3} } is 3

Problem 10: Compute the determinant of the 3×3 matrix below.

\Large{\begin{bmatrix} -4 & 1 & 2 \\ 1 & -3 & 2 \\ -4 & 4 & 0 \end{bmatrix}}
Answer
the determinant of the 3x3 matrix { {-4,1,2},{1,-3,2},{-4,4,0} } is 8

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