Determinants and inverse matrices
Grade 11 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
Read this first
Number table A, 2 by 2
Row 1 is 5, 2; row 2 is 4, 3. The down diagonal (5 to 3) is blue; the up diagonal (4 to 2) is orange.
Esme writes matrix A = [5, 2; 4, 3] in a notebook. The down diagonal gives 5 × 3 and the up diagonal gives 2 × 4. What is det(A)?
Number table A, 2 by 2
Row 1 is 6, 1; row 2 is 3, 4. The down diagonal (6 to 4) is blue; the up diagonal (3 to 1) is orange.
Jun copies matrix A = [6, 1; 3, 4] from the board. The down diagonal gives 6 × 4 and the up diagonal gives 1 × 3. What is det(A)?
Number table A, 2 by 2
Row 1 is 7, 3; row 2 is 2, 5. The down diagonal (7 to 5) is blue; the up diagonal (2 to 3) is orange.
Kira reads matrix A = [7, 3; 2, 5] in a math book. The down diagonal gives 7 × 5 and the up diagonal gives 3 × 2. What is det(A)?
Luz checks matrix A = [8, 3; 5, 2] on a worksheet. What is det(A)?
Noah finds matrix A = [9, 4; 5, 3] in a math book. What is det(A)?
A⁻¹ = (1/det(A)) × [d, -b; -c, a]
Swap the down diagonal, change the signs of the up diagonal, then divide every entry by det(A).
Pia finds the inverse of A = [5, 2; 3, 4], and det(A) = 14. What is the top-right entry of A⁻¹?
Tala finds the inverse of A = [5, 3; 4, 6], and det(A) = 18. What is the top-left entry of A⁻¹?
Esme finds the inverse of A = [6, 4; 1, 3], and det(A) = 14. What is the bottom-right entry of A⁻¹?
Kira checks the table A = [2, 5; 4, 10] before finding its inverse. Does A have an inverse?
- No: det(A) = 0
- Yes: det(A) = -30
- Yes: det(A) = 40
- Yes: det(A) = 0
Luz checks the table A = [2, 3; 6, 1] before finding its inverse. Does A have an inverse?
- Yes: det(A) = -16
- Yes: det(A) = 20
- No: det(A) = 0