Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK20269 May 2026Morning ShiftMathematicsDeterminantsActual

Given P = bmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 bmatrix is the adjoint of a 3 3 matrix A and |A| = 3 , then the value of is:

Options

  1. A-8
  2. B-26
  3. C7
  4. D-25

Correct answer

A. -8

Step-by-step solution

Given P = adj (A) and A is a 3 3 matrix. We know that | adj (A)| = |A|^ n-1 , where n is the order of the matrix. Here, n = 3 and |A| = 3 . |P| = |A|³⁻¹ = |A|^2 = 3^2 = 9 Now, calculating the determinant of matrix P : |P| = vmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 vmatrix Expanding along the first row: |P| = 2(2 3 - 2 3) - (1 3 - 2 1) + 1(1 3 - 2 1) |P| = 2(0) - (1) + 1(1) |P| = 1 - Equating the two values of |P| : 1 - = 9 = -8 Answer: -8

Practice Determinants on Quantrex Academy →

More from Determinants

Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is 2026Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is: 2026Which of the following is correct? 2026If A and B are invertible square matrices of order n, then which of the following is not correct? 2026The system of equations x + 2y = 3 and 2x + 3y = 3 has 2026A value of lying between 0 and 2 and satisfying | array ccc 1+ ^2 & ^2 & 4 4 ^2 & 1+ ^2 & 4 4 ^2 & ^2 & 1+4 4 array |=0 2025If the inverse of [ array ccc -x & 14 x & 7 x 0 & 1 & 0 x & -4 x & -2 x array ] is [ array ccc 2 & 0 & 7 0 & 1 & 0 1 & -2 & 1 array ] , then | array ccc x & x+1 & x+2 x+1 & x+2 & x 2025If the system of equations 2 x+3 y-3 z=3, x+2 y+ z=1,2 x-y+z= has infinitely many solutions, then - = 2025 Full Determinants list All COMEDK PYQs