(Key: correct, incorrect, partially correct.)

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

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