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Class 10 Math Chapter 3 Full Unit Paper 2026 | Matrices and Determinants | Punjab Board New Syllabus 2027
Class 10 Mathematics Chapter 3 Full Unit Paper 2026 is prepared for students following the Punjab Board New Syllabus 2027. This Mathematics Full Unit Paper covers important concepts from Matrices and Determinants and includes objective and subjective-type questions for exam preparation. Students can use this Class 10 Math Chapter 3 Test to practice matrices, determinants, inverse of matrices, matrix operations, and related questions according to the new Punjab Board paper pattern.
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Full Unit Test
Unit 3: Matrices and Determinants
New Board Paper Pattern 2027
Objective Type
Time Allowed: 20 Min.
Max. Marks: 15
Note:
Four possible answer A, B, C and D to each question are given.
The choice which you think is correct, fill that circle front of
that question with Marker or ink pen in the answer book.
Cutting filling two or more circles will result in zero mark in
that question.
(i)
M =
[
]
is a/an __________ matrix.
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
(ii) If At = − A, then A is __________ matrix.
(iii) If
[
]
=
[
]
, then a = :
| a + 2 |
| 3 |
| 7 |
| 3 |
(iv) If A =
[
]
, then order of At is:
| 3 | 1 | 3 |
| 2 | 0 | 2 |
(v) If
[
]
=
[
]
then x =
| x − 1 | 3 |
| 2 | x + 1 |
| −2 | 3 |
| 2 | 0 |
(vi) Which of the following is diagonal matrix?
(vii) (At)t =
(viii) ______ matrix is a special case of a diagonal matrix.
(ix) If A =
[
]
and B =
[
]
then AB =
| 5 | 3 |
| −2 |
| 1 |
(x) If A =
[
]
and B =
[
]
then order of BA is:
| a | b | c |
| d |
| e |
| f |
(xi) If A is of order m-by-n and B is of order n-by-f then AB is of order:
(xii) The property of matrices A + (B + C) = (A + B) + C is called ______ under addition.
(xiii) If A and B are negative of each other then:
(xiv) Inverse of the identity matrix
[
]
is:
| 1 | 0 |
| 0 | 1 |
(xv) (AB)−1 =
Here is a Subjective Part of Paper. Solve it carefull.
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Subjective Type
Time Allowed:
2:10 hours
2:10 hours
(Part-I)
Max. Marks: 60
2. Write short answers to any six (06) questions:
(i)
If
[
]
=
[
]
,
then find the values of a, b, c and d.
| a + 2 | c − 3 |
| b − 1 | d + 4 |
| 5 | 8 |
| 6 | 4 |
(ii)
If A =
[
]
and B =
[
]
,
then verify that
(At)t = A
| 2 | 3 |
| 4 | 5 |
| 7 | 6 |
| 5 | 8 |
(At)t = A
(iii)
Show that L =
[
]
is a symmetric matrix.
| 2 | 3 | 4 |
| 3 | −2 | 5 |
| 4 | 5 | 0 |
(iv)
If
[
]
=
[
]
,
then find the values of p and q.
| p + q | 5 |
| 11 | p − 2q |
| 6 | 5 |
| 11 | 0 |
(v)
If A =
[
]
,
B =
[
]
and C =
[
]
,
then verify that A + B = B + A.
| 2 | 3 |
| −3 | 2 |
| 3 | 4 |
| 5 | 6 |
| 1 | −2 |
| 0 | 5 |
(vi)
If A =
[
]
and B =
[
]
,
then verify that:
(A + B)t = At + Bt.
| 6 | −2 |
| 0 | 3 |
| 8 | −1 |
| 3 | 0 |
(vii)
If A =
[
]
and B =
[
]
,
then show that B is additive inverse of A and A is additive inverse of B.
| 5 | 6 |
| 7 | −2 |
| −5 | −6 |
| −7 | 2 |
(viii)
If A =
[
]
,
B =
[
]
,
then find: AB, if possible.
| a | b |
| c | d |
| l | m |
| n | p |
(ix)
If A =
[
]
and B =
[
]
,
then find AB and its order.
| 5 | 3 |
| −2 |
| 1 |
3. Write short answers to any six (06) questions:
(i)
Find AB and BA, if possible.
A =
[
]
,
B =
[
]
.
| 1 | −2 |
| 3 |
| −4 |
(ii)
Verify the statement AB ≠ BA, using
A =
[
]
,
B =
[
]
and C =
[
]
.
| 5 | 1 |
| −1 | 4 |
| 2 | −1 |
| 0 | 3 |
| 5 | 1 |
| 1 | 4 |
(iii)
Define identity matrix.
(iv)
Solve the following matrix inversion method:
2x + 3y = 13
4x − 5y = −7
2x + 3y = 13
4x − 5y = −7
(v)
Which condition is required for multiplication of two matrices.
(vi)
Define matrix with example.
(vii)
If
[
]
[6 −]
=
[
]
,
then find the values of a and b.
| 4 | a |
| b | 3 |
| 6 |
| 3 |
(viii)
If
[
]
[
]
=
[
]
,
then find the values of x and y.
| x | 1 |
| y | 2 |
| 1 | 0 |
| 3 | −1 |
| 7 | −1 |
| 4 | −2 |
(ix)
Define Singular Matrix with example.
4. Write short answers to any six (06) questions:
(i)
Take any 2 by 2 matrix and check whether it is singular or non-singular. Also find its adjoint.
(ii)
Find the values of each of the determinant.
| 10 | 5 |
| 4 | 6 |
(iii)
Find whether the matrix
A =
[
]
is singular or non-singular.
| 5 | 3 |
| 3 | 2 |
(iv)
Find the value of x when
A =
[
]
is a singular matrix.
| x | 6 |
| 5 | 15 |
(v)
Find multiplicative inverse of the matrix
[
]
| 5 | 0 |
| 0 | 5 |
(vi)
Find the adjoint of the matrix
C =
[
]
| −3 | 5 |
| −3 | 2 |
(vii)
Solve the following by matrix inversion method:
2x + 3y = 13
4x − 5y = −7
2x + 3y = 13
4x − 5y = −7
(viii)
Use Cramer’s rule to solve the system of equations:
2x + 3y = 13
4x − 5y = −7
2x + 3y = 13
4x − 5y = −7
(ix)
Define Symmetric Matrix with example.
(Part-II)
Note: Attempt any two (02) questions.
5:(a)
Show that the following matrices are multiplicative inverse of each other.
[
]
,
[
]
[
| 2 | −1 |
| −3 | 2 |
| 2 | 1 |
| 3 | 2 |
(b)
Take any two linear equations in two variables and solve them by matrix inversion method.
6:(a)
If A =
[
]
,
then find multiplicative inverse of A and verify that
AA−1 = A−1A = I.
| 8 | 5 |
| 4 | 3 |
(b)
Two cyclists are 44 km apart and start out at the same time.
If they go towards one another they meet in 2 hours, but if they go in the same direction the faster overtakes the slower in
71⁄2 hours.
Find their speeds by using matrices.
7:(a)
Two years ago a man was 5 times as old as his son was.
After 6 years he will be 3 times as old as his son.
Find their present ages by using matrices.
(b)
If A =
[
]
,
B =
[
]
,
then verify
(AB)−1 = B−1A−1.
Can we say it is also a Reversal Law of Multiplicative Inverse?
| 2 | 1 |
| 3 | 2 |
| 3 | 4 |
| 2 | 4 |
(Part-III)
Note: Attempt any one (01) question.
8:(a)
Eight years ago Huria’s was
3
4
of Jannat’s age.
After four years Huria’s age will be 6 7 of Jannat’s age.
Find their present ages by using matrices.
After four years Huria’s age will be 6 7 of Jannat’s age.
Find their present ages by using matrices.
(b)
Prove that A =
[
]
and B =
[
]
are multiplicative inverse of each other.
| 4 | −2 |
| −6 | 4 |
| 1 | 12 |
| 32 | 1 |
9:(a)
Solve by matrix inversion method, if possible.
2x + 5y = 19
4x − 3y = −1
2x + 5y = 19
4x − 3y = −1
(b)
Three forces act on a particle and must be in equilibrium i.e.
F1 + F2 + F3 = 0,
where
F1 =
[
]
,
F2 =
[
]
,
F3 =
[
]
.
Find the value of x and y.
| 8 |
| x |
| −2 |
| −7 |
| y |
| −1 |
