Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20227 Jul 2022Evening ShiftMathematicsMatricesActual

If a matrix A satisfies the equation A^3-6 A^2+11 A-6 I=0 , then A⁻¹ can be

Options

  1. A1 4
  2. B41
  3. C31
  4. D1 3 /

Correct answer

D. 1 3 /

Step-by-step solution

aligned & A^3-6 A^2+11 A-6 I=0 & A^3-A^2-5 A^2+5 A+6 A-6 I=0 & A^2[A-I]-5 A[A-I]+6[A-I]=0 & [A-I] [A^2-5 A+6 ]=0 & (A-I)(A-2 I)(A-3 I)=0 aligned A-3 I can be a zero matrix. aligned & & A & =3 I & & A A⁻¹ & =3 A⁻¹ & & I & =3 A⁻¹ & & A A⁻¹ & = 1 3 I aligned

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 AP EAMCET PYQs