JEE Main 2024 — Matrices Questions with Solutions

Let R = x 0 0 0 y 0 0 0 z be a non-zero 3 × 3 matrix, where x sin θ = y sin θ + 2 π 3 = z sin θ + 4 π 3 ≠ 0 , θ ∈ ( 0 ,…

Let A be a 3 × 3 matrix and det A = 2 . If n = det a d j a d j . ... a d j A ⏟ 2024 − times , then the remainder when n…

Let A = 2 1 2 6 2 11 3 3 2 and P = 1 2 0 5 0 2 7 1 5 . The sum of the prime factors of P - 1 AP - 2 I is equal to

Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2. Then |AT A(adj(2 ~A))⁻¹(adj(4 ~B))(adj(AB))⁻¹…

Let α (0, ∞) and A= [arraylll1 & 2 & α \ 1 & 0 & 1 \ 0 & 1 & 2array ]. If det (adj (2 A-A^T ) · adj (A-2 A^T ) )=2⁸, th…

Let A be a 3 × 3 matrix of non-negative real elements such that A [arrayl1 \ 1 \ 1array ]=3 [arrayl1 \ 1 \ 1array ]. Th…

Consider the matrix f x = cos x - sin x 0 sin x cos x 0 0 0 1 . Given below are two statements : Statement I: f ( - x )…

Let A= [arraycc2 & -1 \ 1 & 1array ]. If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal to_________

Let α β ≠ 0 and A= [arrayrrrβ & α & 3 \ α & α & β \ -β & α & 2 αarray ]. If B= [arrayrrr3 α & -9 & 3 α \ -α & 7 & -2 α…

If A is a square matrix of order 3 such that det(A)=3 and det (adj (-4 adj (-3 adj (3 adj ((2 ~A)⁻¹ ) ) ) ) )=2m 3ⁿ, th…