Here are some multiple-choice questions (MCQs) on matrices for 9th and 10th class math students.
Each question is followed by four options,
with the correct answer marked.
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1. If A = [2 3] and B = [1 4], then A + B is:
- (a) [3 7]
- (b) [2 3]
- (c) [1 4]
- (d) [3 4]
- **Correct Answer: (a) [3 7]**
2. A matrix with only one row is called:
- (a) Row matrix
- (b) Column matrix
- (c) Square matrix
- (d) Null matrix
- **Correct Answer: (a) Row matrix**
3. The order of a matrix with 3 rows and 4 columns is:
- (a) 3 × 3
- (b) 3 × 4
- (c) 4 × 4
- (d) 4 × 3
- **Correct Answer: (b) 3 × 4**
4. If A = [3 2] and B = [1 5], then A - B is:
- (a) [2 -3]
- (b) [4 7]
- (c) [2 -5]
- (d) [3 2]
- **Correct Answer: (a) [2 -3]**
5. The transpose of the matrix A = [1 2; 3 4] is:
- (a) [1 3; 2 4]
- (b) [2 1; 4 3]
- (c) [1 2; 4 3]
- (d) [2 4; 1 3]
- **Correct Answer: (a) [1 3; 2 4]**
6. A matrix with all entries zero is called:
- (a) Unit matrix
- (b) Identity matrix
- (c) Zero matrix
- (d) Diagonal matrix
- **Correct Answer: (c) Zero matrix**
7. A square matrix with 1’s on the diagonal and 0’s elsewhere is called:
- (a) Zero matrix
- (b) Diagonal matrix
- (c) Row matrix
- (d) Identity matrix
- **Correct Answer: (d) Identity matrix**
8. Which of the following matrices has an equal number of rows and columns?
- (a) Row matrix
- (b) Square matrix
- (c) Column matrix
- (d) Rectangular matrix
- **Correct Answer: (b) Square matrix**
9. The product of a matrix A and the identity matrix I is:
- (a) Zero matrix
- (b) Transpose of A
- (c) Identity matrix
- (d) Matrix A
- **Correct Answer: (d) Matrix A**
10. If A = [2 3; 4 5], the determinant of A is:
- (a) 2
- (b) -2
- (c) 6
- (d) -6
- **Correct Answer: (b) -2**
11. A matrix with only one column is called:
- (a) Row matrix
- (b) Column matrix
- (c) Null matrix
- (d) Square matrix
- **Correct Answer: (b) Column matrix**
12. If A = [1 2; 3 4] and B = [4 3; 2 1], then A + B is:
- (a) [5 5; 5 5]
- (b) [4 3; 2 1]
- (c) [3 5; 7 9]
- (d) [5 5; 4 4]
- **Correct Answer: (a) [5 5; 5 5]**
13. If A = [4 0; 0 4], what type of matrix is A?
- (a) Zero matrix
- (b) Diagonal matrix
- (c) Unit matrix
- (d) Rectangular matrix
- **Correct Answer: (b) Diagonal matrix**
14. Which of the following is the scalar multiplication of the matrix A = [1 2; 3 4] by 3?
- (a) [3 6; 9 12]
- (b) [3 4; 1 2]
- (c) [1 2; 3 4]
- (d) [0 0; 0 0]
- **Correct Answer: (a) [3 6; 9 12]**
15. The determinant of a 2×2 matrix [a b; c d] is:
- (a) a + b + c + d
- (b) ad - bc
- (c) ab + cd
- (d) None of these
- **Correct Answer: (b) ad - bc**
16. Which of the following represents the inverse of matrix A if A = [1 0; 0 1]?
- (a) [1 0; 0 1]
- (b) [0 0; 0 0]
- (c) [0 1; 1 0]
- (d) None of these
- **Correct Answer: (a) [1 0; 0 1]**
17. If A = [2 4; 1 3] and B = [3 5; 2 6], the element in the first row and second column of A + B is:
- (a) 6
- (b) 5
- (c) 7
- (d) 10
- **Correct Answer: (c) 7**
18. The trace of the matrix A = [3 1; 2 4] is:
- (a) 2
- (b) 4
- (c) 6
- (d) 7
- **Correct Answer: (d) 7**
19. If A and B are two matrices of the same order, then A + B is:
- (a) Not defined
- (b) A scalar
- (c) A matrix of the same order as A and B
- (d) A matrix of a different order
- Correct Answer: (c) A matrix of the same order as A and B
20. The identity matrix for multiplication is:
- (a) [0 0; 0 0]
- (b) [1 1; 1 1]
- (c) [1 0; 0 1]
- (d) None of these
- Correct Answer: (c) [1 0; 0 1]
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1. A matrix with only one row is called:
- (a) Row matrix
- (b) Column matrix
- (c) Square matrix
- (d) Diagonal matrix
- **Correct Answer: (a) Row matrix**
2. A matrix with only one column is called:
- (a) Row matrix
- (b) Column matrix
- (c) Null matrix
- (d) Square matrix
- **Correct Answer: (b) Column matrix**
3. A matrix with the same number of rows and columns is called:
- (a) Square matrix
- (b) Rectangular matrix
- (c) Row matrix
- (d) Column matrix
- **Correct Answer: (a) Square matrix**
4. A matrix with all elements zero is known as a:
- (a) Unit matrix
- (b) Zero matrix
- (c) Identity matrix
- (d) Scalar matrix
- **Correct Answer: (b) Zero matrix**
5. A square matrix with all diagonal elements as 1 and all other elements as 0 is called:
- (a) Diagonal matrix
- (b) Identity matrix
- (c) Null matrix
- (d) Row matrix
- **Correct Answer: (b) Identity matrix**
6. A square matrix in which all elements outside the main diagonal are zero is called:
- (a) Identity matrix
- (b) Null matrix
- (c) Diagonal matrix
- (d) Row matrix
- **Correct Answer: (c) Diagonal matrix**
7. A square matrix in which all elements are zero except the main diagonal elements, which are the same number, is called:
- (a) Scalar matrix
- (b) Diagonal matrix
- (c) Identity matrix
- (d) Zero matrix
- **Correct Answer: (a) Scalar matrix**
8. A matrix with m rows and n columns where m ≠ n is called:
- (a) Square matrix
- (b) Rectangular matrix
- (c) Null matrix
- (d) Scalar matrix
- **Correct Answer: (b) Rectangular matrix**
9. The transpose of a column matrix is a:
- (a) Row matrix
- (b) Square matrix
- (c) Diagonal matrix
- (d) Null matrix
- **Correct Answer: (a) Row matrix**
10. If a matrix has 2 rows and 3 columns, it is called a:
- (a) Square matrix
- (b) Column matrix
- (c) Rectangular matrix
- (d) Row matrix
- **Correct Answer: (c) Rectangular matrix**
11. A square matrix in which all elements in the main diagonal are zero is called:
- (a) Zero matrix
- (b) Scalar matrix
- (c) Identity matrix
- (d) Hollow matrix
- **Correct Answer: (d) Hollow matrix**
12. A matrix in which all elements are the same is known as:
- (a) Identity matrix
- (b) Constant matrix
- (c) Diagonal matrix
- (d) Zero matrix
- **Correct Answer: (b) Constant matrix**
13. A matrix in which each row has the same elements as the previous row is called a:
- (a) Row matrix
- (b) Column matrix
- (c) Symmetric matrix
- (d) Toeplitz matrix
- **Correct Answer: (d) Toeplitz matrix**
14. A matrix that is equal to its own transpose is called:
- (a) Skew-symmetric matrix
- (b) Symmetric matrix
- (c) Zero matrix
- (d) Scalar matrix
- **Correct Answer: (b) Symmetric matrix**
15. A matrix in which the main diagonal elements are zero and the rest are non-zero is called a:
- (a) Identity matrix
- (b) Hollow matrix
- (c) Skew-symmetric matrix
- (d) Null matrix
- **Correct Answer: (b) Hollow matrix**
16. If a matrix is such that all elements satisfy the condition aij =-aji it is called a:
- (a) Symmetric matrix
- (b) Skew-symmetric matrix
- (c) Diagonal matrix
- (d) Identity matrix
- **Correct Answer: (b) Skew-symmetric matrix**
17. A 2×2 matrix with elements [a, 0; 0, b] where \(a\) and \(b\) are non-zero constants is:
- (a) Null matrix
- (b) Diagonal matrix
- (c) Rectangular matrix
- (d) Column matrix
- **Correct Answer: (b) Diagonal matrix**
18. A square matrix with all elements the same along the main diagonal and zero elsewhere is called:
- (a) Diagonal matrix
- (b) Scalar matrix
- (c) Zero matrix
- (d) Identity matrix
- **Correct Answer: (b) Scalar matrix**
19. The matrix [3 0; 0 3] is an example of a:
- (a) Zero matrix
- (b) Scalar matrix
- (c) Row matrix
- (d) Symmetric matrix
- **Correct Answer: (b) Scalar matrix**
20. A matrix with all elements arranged symmetrically about its main diagonal is known as:
- (a) Skew-symmetric matrix
- (b) Symmetric matrix
- (c) Diagonal matrix
- (d) Scalar matrix
- **Correct Answer: (b) Symmetric matrix**
