250+ TOP MCQs on Matrices | Class 12 Maths

Mathematics Multiple Choice Questions on “Matrices”.

1. If the order of the matrix is m×n, then how many elements will there be in the matrix?
a) mn
b) m² n²
c) mn²
d) 2mn
Answer: a
Clarification: The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.

2. Which of the following is a matrix of the order 2×2 where the equation of the elements is given by a_ij=i+j.
a) A=(begin{bmatrix}1&1\1&1end{bmatrix})
b) A=(begin{bmatrix}4&5\4&1end{bmatrix})
c) A=(begin{bmatrix}2&3\3&4end{bmatrix})
d) A=(begin{bmatrix}1&2\1&2end{bmatrix})
Answer: c
Clarification: a₁₁=1+1=2, a₁₂=1+2=3, a₂₁=2+1=3, a₂₂=2+2=4
∴ A=(begin{bmatrix}a_{11}&a_{12}\a_{21}&a_{22} end{bmatrix}=begin{bmatrix}2&3\3&4end{bmatrix}).

3. What is the order of the matrix A=(begin{bmatrix}3&5\7&9end{bmatrix})?
a) 2×3
b) 2×2
c) 3×3
d) 4×4
Answer: b
Clarification: The number of rows (m) and the number of columns (n) in the given matrix A=(begin{bmatrix}3&5\7&9end{bmatrix}) is 2. Therefore, the order of the matrix is 2×2(m×n).

4. The order of the matrix A=(begin{bmatrix}1&5&9\4&8&6end{bmatrix}) is 2×3.
a) True
b) False
Answer: b
Clarification: The given statement is false. In the matrix A=(begin{bmatrix}1&5&9\4&8&6end{bmatrix}) the number of rows(m) is 3 and the number of columns(n) is 2. Therefore, the order of the matrix is 3×2.

5. In a matrix with 9 elements, then the possible ordered pairs are (3, 3), (1, 9), (9, 1).
a) True
b) False
Answer: a
Clarification: The given statement is true. The possible orders in which the matrix can be formed are 3×3,9×1,1×9. Therefore, the ordered pairs are (3,3),(1,9),(9,1).

6. Which of the following is not a possible ordered pair for a matrix with 6 elements.
a) (2,3)
b) (3,2)
c) (1,6)
d) (3,1)
Answer: d
Clarification: The possible orders in which the matrix with 6 elements can be formed are 2×3, 3×2, 1×6, 6×1. Therefore, the possible orders pairs are (2,3), (3,2), (1,6), (6,1). Thus, (3,1) is not possible.

7. Which of the following matrix is of the order 3×4.
a) A=(begin{bmatrix}3&4\3&5\4&5end{bmatrix})
b) A=(begin{bmatrix}1&2&3\5&7&9end{bmatrix})
c) A=(begin{bmatrix}4&5&6 \5&2&6\6&4&7\7&7&1end{bmatrix})
d) A=(begin{bmatrix}1\4\6end{bmatrix})
Answer: c
Clarification: The matrix A=(begin{bmatrix}4&5&6\5&2&6\6&4&7\7&7&1end{bmatrix}) is a 3×4 matrix as it as 3 rows and 4 columns.

8. Consider the matrix A=(begin{bmatrix}2&4&5\1&6&4\2&8&9end{bmatrix}). Find the element a₃₂.
a) 5
b) 6
c) 4
d) 8
Answer: d
Clarification: a₃₂ is the element represented in the form a_ij i is the row number and j is the column number. Therefore, the element a₃₂ is the element in the third row (i=3)and second column (j=2) which is 8.

9. What is the order of the matrix A=(begin{bmatrix}2&3\1&9\5&2end{bmatrix})?
a) 2×3
b) 3×2
c) 2×2
d) 3×3
Answer: b
Clarification: The given matrix A=(begin{bmatrix}2&3\1&9\5&2end{bmatrix}) has 3 rows and 2 columns. Therefore, the order of the matrix is 3×2.

10. Given a matrix A=(begin{bmatrix}2&3&9\3&9&6\1&6&7end{bmatrix}), which of the elements a_ij follows the condition i=j.
a) 9, 9, 1
b) 2, 9, 7
c) 2, 3, 9
d) 2, 3, 1
Answer: b
Clarification: The elements following the condition i=j will have the same row number and column number. The elements are a₁₁, a₂₂, a₃₃ which in the matrix A are 2, 3, 9 respectively.