Category: Class 9

Short Description

This post contains important MCQs from Class 9 Mathematics – Matrices and Determinants.
These questions are helpful for board exams, tests, and revision.

MCQs-Matrices and Determinants

1. The order of a matrix having 3 rows and 4 columns is:
   • A) $$3 \times 3$$
   • B) $$4 \times 3$$
   • C) $$3 \times 4$$
   • D) $$4 \times 4$$
2. A matrix having equal number of rows and columns is called:
   • A) Rectangular matrix
   • B) Column matrix
   • C) Square matrix
   • D) Row matrix
3. A matrix having only one row is called:
   • A) Column matrix
   • B) Square matrix
   • C) Row matrix
   • D) Zero matrix
4. A matrix having only one column is called:
   • A) Row matrix
   • B) Column matrix
   • C) Square matrix
   • D) Identity matrix
5. A matrix whose all elements are zero is called:
   • A) Identity matrix
   • B) Null matrix
   • C) Scalar matrix
   • D) Square matrix
6. The matrix $$\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$$ is called:
   • A) Null matrix
   • B) Scalar matrix
   • C) Identity matrix
   • D) Square matrix
7. If $$A=\begin{bmatrix}2 & 3 \\ 4 & 5\end{bmatrix}$$ then $$A_{12}$$ is:
   • A) 2
   • B) 3
   • C) 4
   • D) 5
8. Two matrices can be added only if they have:
   • A) Same elements
   • B) Same order
   • C) Same determinant
   • D) Same trace
9. If $$A$$ is of order $$2 \times 3$$ and $$B$$ is of order $$2 \times 3$$, then order of $$A+B$$ is:
   • A) $$3 \times 2$$
   • B) $$2 \times 2$$
   • C) $$3 \times 3$$
   • D) $$2 \times 3$$
10. If $$A=\begin{bmatrix}1 & 2 \\ 3 & 4\end{bmatrix}$$ then $$2A$$ is:
    • A) $$\begin{bmatrix}2 & 4 \\ 6 & 8\end{bmatrix}$$
    • B) $$\begin{bmatrix}1 & 4 \\ 3 & 8\end{bmatrix}$$
    • C) $$\begin{bmatrix}2 & 2 \\ 4 & 4\end{bmatrix}$$
    • D) $$\begin{bmatrix}3 & 4 \\ 5 & 6\end{bmatrix}$$
11. If $$A=\begin{bmatrix}a & b \\ c & d\end{bmatrix}$$ then $$|A|$$ equals:
    • A) $$ad+bc$$
    • B) $$ab-cd$$
    • C) $$ad-bc$$
    • D) $$ac-bd$$
12. The determinant of $$\begin{bmatrix}5 & 7 \\ 5 & 7\end{bmatrix}$$ is:
    • A) 35
    • B) 0
    • C) 14
    • D) 10
13. If determinant of a matrix is zero, the matrix is:
    • A) Identity
    • B) Non-singular
    • C) Singular
    • D) Scalar
14. The determinant of identity matrix of order 2 is:
    • A) 0
    • B) 1
    • C) 2
    • D) −1
15. The determinant of $$\begin{bmatrix}1 & 2 \\ 2 & 4\end{bmatrix}$$ is:
    • A) 2
    • B) −2
    • C) 0
    • D) 6

Answers

1. C
2. C
3. C
4. B
5. B
6. C
7. B
8. B
9. D
10. A
11. C
12. B
13. C
14. B
15. C

16. If $$|A| \neq 0$$, then matrix $$A$$ is:
    • A) Singular
    • B) Identity
    • C) Non-singular
    • D) Null
17. The determinant of $$\begin{bmatrix}a & 0 \\ 0 & d\end{bmatrix}$$ is:
    • A) $$a+d$$
    • B) $$ad$$
    • C) $$a-d$$
    • D) 0
18. The determinant of a triangular matrix is equal to:
    • A) Sum of diagonal elements
    • B) Product of diagonal elements
    • C) Zero
    • D) Square of diagonal elements
19. Which of the following is always a square matrix?
    • A) Row matrix
    • B) Column matrix
    • C) Identity matrix
    • D) Rectangular matrix
20. The order of determinant is defined only for:
    • A) Rectangular matrices
    • B) Square matrices
    • C) Row matrices
    • D) Column matrices
21. If $$A$$ is a null matrix, then $$|A|$$ is:
    • A) 1
    • B) −1
    • C) 0
    • D) Undefined
22. Which matrix has determinant always equal to 1?
    • A) Null matrix
    • B) Identity matrix
    • C) Scalar matrix
    • D) Rectangular matrix
23. If $$A$$ is a square matrix, then $$|A^T|$$ is equal to:
    • A) $$-|A|$$
    • B) $$|A|$$
    • C) $$|A|^2$$
    • D) 0
24. If $$|A|=4$$ and $$A$$ is $$2\times2$$, then $$|3A|$$ is:
    • A) 12
    • B) 36
    • C) 24
    • D) 9
25. A determinant is a single:
    • A) Matrix
    • B) Row
    • C) Column
    • D) Number
26. If $$|A|=-3$$, then $$|-A|$$ for a $$2\times2$$ matrix is:
    • A) −3
    • B) 3
    • C) −6
    • D) 6
27. The determinant changes sign if:
    • A) Rows are added
    • B) Columns are multiplied
    • C) Two rows are interchanged
    • D) Two rows are equal
28. If all elements of a row are zero, the determinant is:
    • A) 1
    • B) −1
    • C) 0
    • D) Undefined
29. A determinant having non-zero value is called:
    • A) Singular
    • B) Non-singular
    • C) Null
    • D) Identity
30. The determinant of a scalar matrix of order 2 with scalar $$k$$ is:
    • A) $$k$$
    • B) $$2k$$
    • C) $$k^2$$
    • D) $$k^3$$
31. A square matrix whose determinant is zero is called:
    • A) Identity matrix
    • B) Singular matrix
    • C) Scalar matrix
    • D) Diagonal matrix
32. Which operation is not possible for matrices?
    • A) Addition
    • B) Subtraction
    • C) Multiplication
    • D) Division
33. If $$|A|=1$$, then matrix $$A$$ is:
    • A) Singular
    • B) Identity
    • C) Non-singular
    • D) Null
34. The determinant of $$\begin{bmatrix}a & b \\ b & a\end{bmatrix}$$ is:
    • A) $$a^2+b^2$$
    • B) $$a^2-b^2$$
    • C) $$2ab$$
    • D) 0
35. The determinant of a $$2\times2$$ matrix represents:
    • A) A matrix
    • B) A vector
    • C) A number
    • D) A function