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COMEDK2025MathematicsIndefinite IntegrationActual

If A= [ array lll a & 0 & 0 0 & a & 0 0 & 0 & a array ] then | adj A|=

Options

  1. Aa^2
  2. Ba^6
  3. Ca^9
  4. Da²⁷

Correct answer

B. a^6

Step-by-step solution

The matrix A is a scalar matrix of order n=3 , given by A = aI , where I is the identity matrix of order 3 . The determinant of A is |A| = vmatrix a & 0 & 0 0 & a & 0 0 & 0 & a vmatrix = a^3 . The property of the adjoint of a matrix states that | adj A| = |A|^ n-1 , where n is the order of the square matrix A . Substituting n=3 and |A| = a^3 into the formula: | adj A| = (a^3)³⁻¹ = (a^3)^2 = a^6 . Answer: a^6

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