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Matrices

JEE Main 2026 (Online) 21st January Evening ShiftMCQMedium📈 Topic in 32% papers+4−1
Ques. 1JEE 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?

  1. x = 16, y = 3
  2. x = 5, y = 7
  3. x = 11, y = 2
  4. x = 18, y = 11

Answer

(3) x = 11, y = 2

Solution

Write A = I + N, where N = A - I = bmatrix 2 & -4 \ 1 & -2 bmatrix

N2 = bmatrix 4 - 4 & -8 + 8 \ 2 - 2 & -4 + 4 bmatrix = O

∵ I and N commute and N2 = O,

A15 = (I + N)15 = I + 15N

= bmatrix 31 & -60 \ 15 & -29 bmatrix

A15 + B = bmatrix 2 & -11 \ 2 & -11 bmatrix

both equations reduce to 2x - 11y = 0

Checking the options, only x = 11, y = 2 satisfies 2(11) - 11(2) = 0.

Answer: (3)

Keep practising — Matrices

Ques. 2JEE 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. 3JEE 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 :

  1. 44
  2. 39
  3. 52
  4. 53
Ques. 4JEE 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 :

  1. bmatrix 257 & -64 \ 514 & -127 bmatrix
  2. bmatrix 766 & -255 \ 1530 & -509 bmatrix
  3. bmatrix 1025 & -511 \ 2024 & -1024 bmatrix
  4. bmatrix 4 & -1 \ 6 & -1 bmatrix
Ques. 5JEE Main 2025, 2 April (Evening Shift)

Let A be a 3 3 real matrix such that A2(A - 2I) - 4(A - I) = O, where I and O are the identity and null matrices, respectively. If A5 = A2 + A + I, where , , and are real constants, then + + is equal to :

  1. 76
  2. 12
  3. 4
  4. 20
Ques. 6JEE Main 2025, 29 January (Morning Shift)

Let S = \m Z : Am2 + Am = 3I - A-6 \, where A = bmatrix 2 & -1 \ 1 & 0 bmatrix. Then n(S) is equal to .

Ques. 7JEE Main 2025, 29 January (Evening Shift)

Let A = [aij] be a matrix of order 3 3, with aij = ( 2)i+j. If the sum of all the elements in the third row of A2 is + 2, , Z, then + is equal to :

  1. 210
  2. 280
  3. 224
  4. 168
Ques. 8JEE Main 2025, 28 January (Morning Shift)

Let M denote the set of all real matrices of order 3 3 and let S = \-3, -2, -1, 1, 2\. Let S1 = \A = [aij] M : A = AT and aij S, i, j\, S2 = \A = [aij] M : A = -AT and aij S, i, j\, S3 = \A = [aij] M : a11 + a22 + a33 = 0 and aij S, i, j\. If n(S1 S2 S3) = 125 , then equals .

Ques. 9JEE Main 2025, 28 January (Evening Shift)

Let A = bmatrix 1 2 & -2 \ 0 & 1 bmatrix and P = bmatrix & - \ & bmatrix, > 0. If B = PAP , C = P B10P and the sum of the diagonal elements of C is mn, where (m, n) = 1, then m + n is :

  1. 127
  2. 2049
  3. 258
  4. 65
Ques. 10JEE Main 2025, 24 January (Morning Shift)

Let A be a 3 3 matrix such that XTAX=O for all nonzero 3 1 matrices X= bmatrixx\ \ bmatrix. If A bmatrix1\\1\\1 bmatrix= bmatrix1\\4\\-5 bmatrix, A bmatrix1\\2\\1 bmatrix= bmatrix0\\4\\-8 bmatrix, and (adj(2(A+I)))=2 3 5 , , , N, then 2+ 2+ 2 is

Ques. 11JEE Main 2025, 24 January (Evening Shift)

Let A=[aij] be a square matrix of order 2 with entries either 0 or 1. Let E be the event that A is an invertible matrix. Then the probability P(E) is :

  1. 38
  2. 18
  3. 316
  4. 58

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