Matrices and Determinants is a high-weightage and conceptually important chapter in JEE Main Mathematics. The questions are usually straightforward but require clarity in concepts and careful calculation. Topics such as algebra of matrices, determinant evaluation, inverse of matrices, and properties of adjoint are commonly tested.
Below are some important problems that aspirants should practise while preparing for JEE Main 2026.
The syllabus includes matrices, types of matrices, algebra of matrices, determinants of order two and three, evaluation of determinants, area of triangles using determinants, adjoint and inverse of a square matrix, and the test of consistency and solution of simultaneous linear equations using matrices.
Question 1
Given matrices
A = [[1, 2], [3, 4]]
B = [[4, -2], [1, 1]]
Find AB minus BA.
Answer
The result is [[8, 0], [12, -8]].
By calculating AB and BA separately and subtracting, the final matrix is obtained.
Question 2
If A = [[1, x], [3, 4]] and det(A) = 3, find the real values of x.
Answer
The values of x are 2 and minus 2.
Using the determinant formula gives x squared minus 1 equals 3.
Question 3
If A = [[2, k], [1, 3]] and A is singular, find k.
Answer
The value of k is 6.
A matrix is singular when its determinant is zero.
Question 4
Find the determinant of
A = [[1, 2, 3], [0, 1, 4], [5, 6, 0]].
Answer
The determinant is 1.
This can be solved using expansion or row operations.
Question 5
If
A inverse = [[4, -1], [2, 1]]
find ad minus bc and the original matrix A.
Answer
The value of ad minus bc is one by six.
The original matrix is [[1/6, 1/6], [-1/3, 2/3]].
This uses the formula for inverse of a two by two matrix.
Question 6
Let A = [[2, 3], [4, k]]. If det(A) = 10, find k.
Answer
The value of k is 11.
The determinant equation gives 2k minus 12 equals 10.
Question 7
If A = [[1, 2], [3, 4]] and I is the identity matrix, find A squared minus 5A plus 6I.
Answer
The result is 8 times the identity matrix.
Question 8
For
A = [[x, 2, 1], [1, x, 2], [2, 1, x]],
find det(A).
Answer
The determinant is x cubed minus 6x plus 9.
Question 9
If det(A) = 5 for a three by three matrix, find det(3A).
Answer
The value is 135.
This uses the property that det(cA) equals c power n times det(A).
Question 10
If B is the adjoint of matrix A and det(A) equals minus 5, find det(B).
Answer
The value is 25.
For a three by three matrix, determinant of adjoint equals determinant squared.
Regular practice of such standard problems can significantly boost confidence and accuracy in the JEE Main examination.
