Matrices Practice Questions
Thanaweya Amma (Egypt) · Thanaweya Mathematics · 145 free MCQs with instant results and detailed explanations.
145
Total
52
Easy
65
Medium
28
Hard
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Sample Questions from Matrices
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Q1
Easy
What is the result of adding two matrices A and B if A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?
A.
[[6, 8], [10, 12]]
B.
[[5, 6], [3, 4]]
C.
[[1, 2], [3, 4]]
D.
[[8, 10], [10, 12]]
Show Answer & Explanation
Correct Answer: A
When adding two matrices, you add their corresponding elements. For A and B, 1+5=6, 2+6=8, 3+7=10, and 4+8=12, resulting in [[6, 8], [10, 12]].
Q2
Easy
If matrix C is defined as C = [[3, 4], [2, 1]], what is the value of C[1][0]?
A.
3
B.
2
C.
4
D.
1
Show Answer & Explanation
Correct Answer: B
In matrix C, the element C[1][0] refers to the second row and the first column, which is 2.
Q3
Easy
Which of the following matrices is a square matrix?
A.
[[1, 2, 3], [4, 5, 6]]
B.
[[1, 0], [0, 1]]
C.
[[7, 8], [9, 10], [11, 12]]
D.
[[0]]
Show Answer & Explanation
Correct Answer: B
A square matrix has the same number of rows and columns. Option B has 2 rows and 2 columns, making it a square matrix.
Q4
Medium
If A = [[2, 3], [1, 4]] and B = [[1, 0], [2, 3]], what is the result of A + B?
A.
[[3, 3], [3, 7]]
B.
[[3, 3], [1, 7]]
C.
[[2, 3], [3, 4]]
D.
[[1, 3], [3, 4]]
Show Answer & Explanation
Correct Answer: A
Matrix addition is performed element-wise. Therefore, A + B = [[2+1, 3+0], [1+2, 4+3]] = [[3, 3], [3, 7]].
Q5
Medium
What is the determinant of the matrix A = [[5, 2], [4, 3]]?
A.
7
B.
10
C.
1
D.
-1
Show Answer & Explanation
Correct Answer: A
The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. Here, det(A) = (5*3) - (2*4) = 15 - 8 = 7.
Q6
Medium
If matrix A = [[1, 2], [3, 4]], what is A^2 (A squared)?
A.
[[7, 10], [15, 22]]
B.
[[10, 14], [14, 20]]
C.
[[4, 6], [12, 16]]
D.
[[1, 2], [3, 4]]
Show Answer & Explanation
Correct Answer: A
Matrix A squared is calculated by multiplying A by itself: A * A = [[1*1 + 2*3, 1*2 + 2*4], [3*1 + 4*3, 3*2 + 4*4]] = [[7, 10], [15, 22]].
Q7
Medium
If A is a 3x3 matrix and its transpose is A^T, then which of the following is true?
A.
A + A^T is symmetric.
B.
A - A^T is symmetric.
C.
A^T does not exist.
D.
A^T is always diagonal.
Show Answer & Explanation
Correct Answer: A
A matrix sum A + A^T produces a symmetric matrix since the elements a_ij and a_ji are added together, which results in symmetry.
Q8
Hard
Given the matrices A = [[2, 3], [1, 4]] and B = [[1, 0], [0, 1]], what is the product AB?
A.
[[2, 3], [1, 4]]
B.
[[2, 3, 0], [1, 4, 0]]
C.
[[2, 3], [0, 4]]
D.
[[2, 3], [1, 0]]
Show Answer & Explanation
Correct Answer: A
The product AB is calculated by multiplying corresponding elements and summing them. Since B is the identity matrix, AB = A, which means the answer is [[2, 3], [1, 4]].
Q9
Hard
If matrix C = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] is transformed to D by the operation D = C^2 - 2C, what is the (2, 2) element of matrix D?
A.
16
B.
11
C.
9
D.
14
Show Answer & Explanation
Correct Answer: A
To find D, we first compute C^2 and then subtract 2C. The (2, 2) element of D is calculated as: (4 + 10 + 18) - 2 * (2 + 5 + 8) = 32 - 16 = 16.
Q10
Hard
Consider the matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]. What is the result of the matrix multiplication AB?
A.
[[19, 22], [43, 50]]
B.
[[23, 34], [31, 46]]
C.
[[43, 50], [19, 22]]
D.
[[35, 40], [55, 64]]
Show Answer & Explanation
Correct Answer: A
The product of the matrices A and B is calculated as follows: AB = [[(1*5 + 2*7), (1*6 + 2*8)], [(3*5 + 4*7), (3*6 + 4*8)]] = [[19, 22], [43, 50]]. Thus, option A is correct.
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Matrices — Thanaweya Amma (Egypt) Thanaweya Mathematics Practice Questions Online
This page contains 145 practice MCQs for the chapter Matrices in Thanaweya Amma (Egypt) Thanaweya Mathematics. The questions are organized by difficulty — 52 easy, 65 medium, 28 hard — so you can choose the right level for your preparation.
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