Matrices Practice Questions
A-Levels · A-Level Further Mathematics · 149 free MCQs with instant results and detailed explanations.
149
Total
51
Easy
73
Medium
25
Hard
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Sample Questions from Matrices
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Q1
Easy
What is the determinant of the matrix \( A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \)?
A.
-2
B.
2
C.
7
D.
1
Show Answer & Explanation
Correct Answer: A
The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is calculated as \( ad - bc \). For this matrix, it is \( (1)(4) - (2)(3) = 4 - 6 = -2 \).
Q2
Easy
If matrix \( B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \) is multiplied by itself, what is the resulting matrix?
A.
\( \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \)
B.
\( \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \)
C.
\( \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \)
D.
\( \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \)
Show Answer & Explanation
Correct Answer: A
Multiplying matrix B by itself gives \( B \times B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \times \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} = \begin{pmatrix} (-1)(0) + (1)(-1) & (0)(1) + (1)(0) \\ (-1)(0) + (0)(-1) & (0)(1) + (0)(0) \end{pmatrix} = \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \).
Q3
Easy
Which of the following is a property of an invertible matrix?
A.
Its determinant is zero.
B.
It has no eigenvalues.
C.
Its determinant is not equal to zero.
D.
It is always a square matrix.
Show Answer & Explanation
Correct Answer: C
A matrix is invertible if and only if its determinant is not equal to zero. Therefore, option C correctly describes a critical property of invertible matrices.
Q4
Medium
If A is a 2x2 matrix given by A = [[2, 3], [1, 4]], what is the determinant of matrix A?
A.
5
B.
10
C.
2
D.
11
Show Answer & Explanation
Correct Answer: A
The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. Here, it is (2*4) - (3*1) = 8 - 3 = 5.
Q5
Medium
Which of the following matrices is the inverse of the matrix B = [[1, 2], [3, 4]]?
A.
[[-2, 1], [1.5, -0.5]]
B.
[[4, -2], [-3, 1]]
C.
[[0.5, 1], [1.5, 2]]
D.
[[-4, 2], [3, -1]]
Show Answer & Explanation
Correct Answer: A
The inverse of a 2x2 matrix [[a, b], [c, d]] is given by (1/det(B)) * [[d, -b], [-c, a]]. The determinant is -2, and the inverse is [[-2, 1], [1.5, -0.5]].
Q6
Medium
If C = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], what is the matrix C multiplied by the scalar 2?
A.
[[2, 4, 6], [0, 2, 8], [10, 12, 0]]
B.
[[1, 2, 3], [0, 1, 4], [5, 6, 0]]
C.
[[3, 6, 9], [0, 3, 12], [15, 18, 0]]
D.
[[2, 2, 2], [0, 2, 4], [5, 6, 0]]
Show Answer & Explanation
Correct Answer: A
Multiplying a matrix by a scalar means multiplying each element of the matrix by that scalar. Here, 2*C = [[2*1, 2*2, 2*3], [0, 2*1, 2*4], [2*5, 2*6, 2*0]], resulting in [[2, 4, 6], [0, 2, 8], [10, 12, 0]].
Q7
Medium
What is the rank of the matrix D = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?
A.
3
B.
2
C.
1
D.
0
Show Answer & Explanation
Correct Answer: B
The rank of a matrix is the maximum number of linearly independent row or column vectors. For matrix D, rows are linearly dependent, leading to a rank of 2.
Q8
Hard
Given a 2x2 matrix A = [[3, 2], [1, 4]], what is the determinant of matrix A?
A.
10
B.
5
C.
1
D.
8
Show Answer & Explanation
Correct Answer: A
The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. For matrix A, the determinant is (3*4) - (2*1) = 12 - 2 = 10.
Q9
Hard
For the matrices P = [[1, 2], [3, 4]] and Q = [[5, 6], [7, 8]], what is the product PQ?
A.
[[19, 22], [43, 50]]
B.
[[23, 28], [31, 38]]
C.
[[43, 50], [19, 22]]
D.
[[34, 38], [70, 78]]
Show Answer & Explanation
Correct Answer: A
Matrix multiplication is performed by taking the dot product of rows from the first matrix with columns from the second. The resulting matrix is [[(1*5 + 2*7), (1*6 + 2*8)], [(3*5 + 4*7), (3*6 + 4*8)]], resulting in [[19, 22], [43, 50]].
Q10
Hard
If matrix M is defined as M = [[0, 1], [-1, 0]], what is the result of applying the transformation M to the vector v = [3, 4]?
A.
[4, -3]
B.
[-4, 3]
C.
[3, 4]
D.
[0, 0]
Show Answer & Explanation
Correct Answer: A
The transformation M rotates the vector v by 90 degrees counterclockwise. Applying M to v gives M * v = [[0, 1], [-1, 0]] * [3, 4] = [0*3 + 1*4, -1*3 + 0*4] = [4, -3].
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Matrices — A-Levels A-Level Further Mathematics Practice Questions Online
This page contains 149 practice MCQs for the chapter Matrices in A-Levels A-Level Further Mathematics. The questions are organized by difficulty — 51 easy, 73 medium, 25 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.