Matrices

JEE Main 2026 (Online) 2nd April Evening ShiftNumericalMedium📈 Topic in 8% papers+4

Ques. 1JEE Main 2026, 2 April (Evening Shift)

Consider the matrices A= bmatrix2 & -2\ 4 & -2 bmatrix and B= bmatrix3 & 9\ 1 & 3 bmatrix. If matrices P and Q are such that PA=B and AQ=B, then the absolute value of the sum of the diagonal elements of 2(P+Q) is .

Answer

Solution

|A|=-4+8=4 0, A-1= 14 bmatrix-2&2\\-4&2 bmatrix

PA=B P=BA-1= 14 bmatrix3&9\\1&3 bmatrix bmatrix-2&2\\-4&2 bmatrix= 14 bmatrix-42&24\\-14&8 bmatrix

tr(P)= -42+84=- 172

AQ=B Q=A-1B= 14 bmatrix-2&2\\-4&2 bmatrix bmatrix3&9\\1&3 bmatrix= 14 bmatrix-4&-12\\-10&-30 bmatrix

tr(Q)= -4-304=- 172 (as expected, tr(BA-1)=tr(A-1B))

tr (2(P+Q) )=2 (- 172- 172 )=-34

Absolute value =34

Answer: 34

Keep practising — Matrices

Ques. 2JEE Main 2026, 28 January (Morning Shift)

Let A, B and C be three 2 × 2 matrices with real entries such that B = (I + A)-1 and A + C = I. If BC = bmatrix 1 & -5 \ -1 & 2 bmatrix and CB bmatrix x1 \ x2 bmatrix = bmatrix 12 \ -6 bmatrix, then x1 + x2 is

4
2
0
−2

Ques. 3JEE Main 2026, 28 January (Evening Shift)

Let A = bmatrix 3 & -4 \ 1 & -1 bmatrix and B be two matrices such that A100 = 100B + I. Then the sum of all the elements of B100 is

Ques. 4JEE Main 2026, 24 January (Morning Shift)

The number of 3 2 matrices A, which can be formed using the elements of the set \-2, -1, 0, 1, 2\ such that the sum of all the diagonal elements of ATA is 5, is

Ques. 5JEE Main 2026, 23 January (Evening Shift)

Let A = bmatrix 0 & 2 & -3 \ -2 & 0 & 1 \ 3 & -1 & 0 bmatrix and B be a matrix such that B(I - A) = I + A. Then the sum of the diagonal elements of BTB is equal to

Ques. 6JEE Main 2026, 22 January (Morning Shift)

If A = bmatrix 2 & 3 \ 3 & 5 bmatrix, then the determinant of the matrix (A2025 - 3 A2024 + A2023 ) is

Ques. 7JEE Main 2026, 21 January (Morning Shift)

For some , R, let A = bmatrix & 2 \ 1 & 2 bmatrix and B = bmatrix 1 & 1 \ 1 & bmatrix be such that A2 - 4A + 2I = B2 - 3B + I = O. Then ( ( adj(A3 - B3)))2 is equal to .

Ques. 8JEE Main 2026, 21 January (Evening Shift)

For the matrices A = bmatrix 3 & -4 \ 1 & -1 bmatrix and B = bmatrix -29 & 49 \ -13 & 18 bmatrix, if (A15 + B) bmatrix x \ y bmatrix = bmatrix 0 \ 0 bmatrix, then among the following which one is true?

x = 16, y = 3
x = 5, y = 7
x = 11, y = 2
x = 18, y = 11

Ques. 9JEE Main 2025, 4 April (Morning Shift)

Let A = bmatrix & 0 & - \ 0 & 1 & 0 \ & 0 & bmatrix. If for some (0, ), A2 = AT, then the sum of the diagonal elements of the matrix (A + I)3 + (A - I)3 - 6A is equal to .

Ques. 10JEE Main 2025, 4 April (Evening Shift)

Let the matrix A = bmatrix 1 & 0 & 0 \ 1 & 0 & 1 \ 0 & 1 & 0 bmatrix satisfy An = An-2 + A2 - I for n 3. Then the sum of all the elements of A50 is :

Ques. 11JEE Main 2025, 2 April (Morning Shift)

Let A = bmatrix & -1 \ 6 & bmatrix, > 0, such that (A) = 0 and + = 1. If I denotes 2 2 identity matrix, then the matrix (I + A)8 is :

bmatrix 257 & -64 \ 514 & -127 bmatrix
bmatrix 766 & -255 \ 1530 & -509 bmatrix
bmatrix 1025 & -511 \ 2024 & -1024 bmatrix
bmatrix 4 & -1 \ 6 & -1 bmatrix

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