Matrices and Determinants Practice Questions
HSC/SSC (Bangladesh) · HSC Mathematics · 149 free MCQs with instant results and detailed explanations.
149
Total
44
Easy
80
Medium
25
Hard
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Sample Questions from Matrices and Determinants
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Q1
Easy
What is the determinant of the matrix A = [[1, 2], [3, 4]]?
A.
-2
B.
2
C.
0
D.
5
Show Answer & Explanation
Correct Answer: A
The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. Here, for A, it is (1*4) - (2*3) = 4 - 6 = -2.
Q2
Easy
If the matrix B = [[2, 0], [0, 3]] is multiplied by the scalar 2, what will be the resulting matrix?
A.
[[4, 0], [0, 6]]
B.
[[2, 0], [0, 3]]
C.
[[0, 0], [0, 0]]
D.
[[1, 0], [0, 1]]
Show Answer & Explanation
Correct Answer: A
When a matrix is multiplied by a scalar, each element of the matrix is multiplied by that scalar. Here, 2*2 = 4 and 2*3 = 6, leading to [[4, 0], [0, 6]].
Q3
Easy
Which of the following matrices is symmetric?
A.
[[1, 2], [2, 1]]
B.
[[1, 2], [3, 4]]
C.
[[0, 5], [6, 0]]
D.
[[7, 8, 9], [10, 11, 12]]
Show Answer & Explanation
Correct Answer: A
A matrix is symmetric if it is equal to its transpose. For matrix A, the transpose is the same as the original matrix: [[1, 2], [2, 1]].
Q4
Medium
If A is a 2x2 matrix defined as A = [[2, 3], [1, 4]], what is the determinant of A?
A.
5
B.
10
C.
11
D.
8
Show Answer & Explanation
Correct Answer: A
The determinant of a 2x2 matrix [[a, b], [c, d]] is calculated as ad - bc. Here, a=2, b=3, c=1, d=4. Thus, det(A) = (2*4) - (3*1) = 8 - 3 = 5.
Q5
Medium
Which of the following statements about the inverse of a matrix is TRUE?
A.
A matrix must be square to have an inverse.
B.
The inverse of a matrix always exists.
C.
The inverse of a matrix is always a diagonal matrix.
D.
Only singular matrices have inverses.
Show Answer & Explanation
Correct Answer: A
A matrix must be square (having the same number of rows and columns) to have an inverse. Non-square matrices cannot have an inverse.
Q6
Medium
If A is a 3x3 matrix given by A = [[1, 2, 3], [0, 1, 4], [5, 6, 0]], what is the value of the determinant of A?
A.
10
B.
18
C.
30
D.
15
Show Answer & Explanation
Correct Answer: B
To find the determinant of a 3x3 matrix, use the rule of Sarrus or cofactor expansion. Here, the determinant calculates to 18 using those methods.
Q7
Medium
If two matrices A and B are such that AB = I (identity matrix), what can we conclude about matrices A and B?
A.
A is the inverse of B.
B.
B is the inverse of A.
C.
Both A and B are singular matrices.
D.
Both A and B must be square matrices.
Show Answer & Explanation
Correct Answer: D
For the product of two matrices to result in an identity matrix, both matrices must be square. This ensures that the dimensions are compatible for matrix multiplication.
Q8
Hard
If the matrix C = [[x, 2], [3, 4]] is singular, what is the value of x?
A.
6
B.
8
C.
12
D.
5
Show Answer & Explanation
Correct Answer: A
A matrix is singular if its determinant is zero. For C, the determinant is given by (x*4 - 2*3) = 4x - 6. Setting this equal to zero gives 4x - 6 = 0, leading to x = 6.
Q9
Hard
If A is a 3x3 matrix given by A = [[2, 1, 3], [1, 0, 2], [4, 5, 6]], what is the value of the determinant of matrix A?
A.
4
B.
10
C.
12
D.
20
Show Answer & Explanation
Correct Answer: A
The determinant of a 3x3 matrix can be calculated using the formula |A| = a(ei-fh) - b(di-fg) + c(dh-eg). For A, the determinant evaluates to 4, confirming option A as correct.
Q10
Hard
Consider the matrices B = [[1, 2], [3, 4]] and C = [[5, 6], [7, 8]]. What is the trace of the product matrix BC?
A.
19
B.
22
C.
26
D.
30
Show Answer & Explanation
Correct Answer: B
The trace of a matrix is the sum of its diagonal elements. The product BC results in a matrix whose trace is 22, making option B the correct answer.
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Matrices and Determinants — HSC/SSC (Bangladesh) HSC Mathematics Practice Questions Online
This page contains 149 practice MCQs for the chapter Matrices and Determinants in HSC/SSC (Bangladesh) HSC Mathematics. The questions are organized by difficulty — 44 easy, 80 medium, 25 hard — so you can choose the right level for your preparation.
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