Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2013MathematicsMatrices

If the determinant of the adjoint of a (real) matrix of order 3 is 25 , then the determinant of the inverse of the matrix is

Options

  1. A0.2
  2. B5
  3. C1 [5] 625
  4. D0.2

Correct answer

D. 0.2

Step-by-step solution

Given, the determinant of the adjoint of a (real) matrix of order 3 is 25 . i.e., | adj A|=25...(i) We know that, | adj A|=|A|^ n-1 (here, n=3 ) |A|³⁻¹=|A|²=25 [from Eq. (i)] |A|= 5 |A⁻¹ |=|A|⁻¹= 1 |A| = 1 5 = 0.2 (by property)

Practice Matrices on Quantrex Academy →

More from Matrices

Given A = bmatrix x & 1 & -2 bmatrix and B = bmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 bmatrix . If ABA^t = [-20] then the value of x is: 2026If the matrix M = bmatrix x+5 & a & -4 -2 & 0 & b c & 6 & y+1 bmatrix is a skew symmetric matrix, the value of the expression ab + c^2 - xy is: 2026Matrix A = bmatrix 1 & 1 & 2 1 & -2 & 2 1 & 0 & -1 bmatrix , Given M₂₂ and A₃₂ are the minor and cofactor of the adjoint matrix of A respectively then the value of the expression M 2026If A and B are two square matrices of the same order such that AB = A and BA = B , then (A + B)^2 is equal to: 2026Given the matrices A = bmatrix 1 & 0 & 1 0 & 1 & 0 1 & 0 & 2 bmatrix and B = bmatrix 2 & 1 & 0 1 & 1 & 2 0 & 2 & 1 bmatrix , then the minor M₂₃ of the matrix (A B⁻¹)⁻¹ is: 2026Given A = pmatrix 1 & 2 2 & 3 pmatrix and f(x) = x^2 - 2x - 3 then f(A) is: 2026If the system of equations 2 x+p y+6 z=8, x+2 y+q z=5 and x+y+3 z=4 has infinitely many solutions, then p = 2025If x^a y^b=e^m, x^c y^d=e^n, ₁= | array ll m & b n & d array |, ₂= | array ll a & m c & n array |, ₃= | array ll a & b c & d array | , then the values of x and y are respectively ( 2025 Full Matrices list All KCET PYQs