# Quiz: Determinants

## This quiz is designed to test basic properties of determinants.

Discuss this quiz

(Key: correct, incorrect, partially correct.)

1. Let be a matrix with determinant 6. What is the determinant of (the inverse of )?
1. 1/6.
• CORRECT.
2. 6.
3. 0.
4. 30.
5. 25/6.
6. 1.
7. Insufficient information to solve the question.
2. Let be a matrix with determinant , and let be a matrix with determinant 4. What is the determinant of ?
1. 24.
• CORRECT.
2. 10.
3. 0.
4. 1/6.
5. 1/4.
6. 1.
7. Insufficient information to solve the question.
3. Let be a matrix with determinant 6, and let be a matrix with determinant 4. What is the determinant of A+B?
1. 24.
2. 10.
3. 0.
4. 1/6.
5. 1/4.
6. 1.
7. Insufficient information to solve the question.
• CORRECT.
4. Let be a matrix with determinant 3. What is the determinant of -A?
1. 3.
• CORRECT.
2. -3.
3. 1/3.
4. 0.
5. 1.
6. -1.
7. Insufficient information to solve the question.
5. Let be a matrix with determinant 3. What is the determinant of 2A?
1. 48.
• CORRECT.
2. 6.
3. 3.
4. 24.
5. 12.
6. 196,608.
7. Insufficient information to solve the question.
6. Let be a matrix with determinant 3. What is the determinant of A^t (the transpose of )?
1. 3.
• CORRECT.
2. 3^t.
3. 12.
4. 1/3.
5. 27.
6. 81.
7. Insufficient information to solve the question.
7. Let be a matrix with determinant 3. Let be the matrix formed by swapping the second and third rows of . What is ?
1. -3.
• CORRECT.
2. 3.
3. 0.
4. 1/3.
5. 6.
6. 2.
7. Insufficient information to solve the question.
8. Let be a matrix with determinant 3. Let be the matrix formed by multiplying the fourth row of by 2. What is ?
1. 6.
• CORRECT.
2. 3.
3. 3/2.
4. -48.
5. 48.
6. -6.
7. Insufficient information to solve the question.
9. Let be a matrix with determinant 3. Let be the matrix formed by dividing the fourth row of by 2. What is ?
1. 3/2.
• CORRECT.
2. 3.
3. 6.
4. 3/16.
5. 3/4.
6. -3.
7. Insufficient information to solve the question.
10. Let be a matrix with determinant 3. Let be the matrix formed by adding two copies of the third row to the first. What is ?
1. 3.
• CORRECT.
2. 6.
3. 0.
4. -3.
5. -6.
6. 9.
7. Insufficient information to solve the question.
11. Let be a matrix with determinant 3. Let be the matrix formed by subtracting two copies of the third row from the first. What is ?
1. 3.
• CORRECT.
2. 6.
3. 0.
4. -3.
5. -6.
6. -9.
7. Insufficient information to solve the question.
12. Let be a matrix. The relationship between determinant and invertibility is
1. is invertible if and only if its determinant is non-zero.
• CORRECT.
2. is invertible if its determinant is non-zero, but not conversely.
3. The determinant of is non-zero if is invertible, but not conversely.
4. is invertible if and only if its determinant is zero.
5. is invertible if its determinant is zero, but not conversely.
6. The determinant of is zero if is invertible, but not conversely.
7. There is no connection between the two concepts.