## 1. What is the determinant of a 2×2 matrix [[a,b],[c,d]]?

### Answer:

### Explanation:

Determinant of [[a,b],[c,d]] is ad-bc.

## 2. The determinant of an identity matrix of any order is:

### Answer:

### Explanation:

Determinant of the identity matrix is always 1.

## 3. If two rows (or columns) of a determinant are identical, then its value is:

### Answer:

### Explanation:

If two rows or columns are identical, the determinant value is 0.

## 4. What is the result of interchanging two rows (or columns) of a determinant?

### Answer:

### Explanation:

Interchanging two rows or columns changes the sign of the determinant.

## 5. The determinant of a singular matrix is:

### Answer:

### Explanation:

A matrix is singular if its determinant is zero.

## 6. If each element of a row (or column) of a determinant is multiplied by 'k', the determinant:

### Answer:

### Explanation:

The determinant value gets multiplied by the factor 'k'.

## 7. If A is a matrix of order 3×3, the determinant of 2A is:

### Answer:

### Explanation:

The determinant gets multiplied by 2^3 = 8.

## 8. If det(A) = 5, then the determinant of its inverse, det(A^(-1)), is:

### Answer:

### Explanation:

det(A^(-1)) is the reciprocal of det(A).

## 9. For any matrix A, det(At) is:

### Answer:

### Explanation:

The determinant of the transpose of A is the same as the determinant of A.

## 10. If two matrices A and B are of the same order, then det(A+B) is:

### Answer:

### Explanation:

The determinant of the sum is not generally the sum of the determinants.

## 11. A determinant remains unchanged if:

### Answer:

### Explanation:

This means taking the transpose, which doesn’t change the determinant value.

## 12. For any 2×2 matrix [[a,b],[c,d]], if det(A) = 0, then:

### Answer:

### Explanation:

Because ad-bc = 0.

## 13. If A and B are both 3×3 matrices, then det(AB) is:

### Answer:

### Explanation:

The determinant of the product is the product of the determinants.

## 14. The determinant value of the matrix [[2,4],[1,2]] is:

### Answer:

### Explanation:

Using the formula, 2*2 – 4*1 = 0.

## 15. If a determinant has a row of zeros, its value is:

### Answer:

### Explanation:

Any determinant with a full row or column of zeros has a value of 0.

## 16. If B is obtained from A by adding a row of A multiplied by k to another row, then det(B) is:

### Answer:

### Explanation:

Elementary row operations of this type don't change the determinant.

## 17. For a triangular matrix (either lower or upper triangular), the determinant is:

### Answer:

### Explanation:

For a triangular matrix, the determinant is the product of its diagonal elements.

## 18. The value of the determinant [[0,1,2],[3,4,5],[6,7,8]] is:

### Answer:

### Explanation:

This determinant has two identical rows when expanded, making its value 0.

## 19. If A is a 3×3 matrix and k is a scalar, then det(kA) is:

### Answer:

### Explanation:

For a 3×3 matrix, the factor k is raised to the power of the order.

## 20. The determinant value of the 2×2 zero matrix is:

### Answer:

### Explanation:

The determinant of the zero matrix is always 0.