MHT CET202526 Apr 2025Morning ShiftMathematicsMatricesActual

Matrix A is non-singular matrix and (A-3 I)(A-5 I)=0 , then 15 8 A⁻¹= _________

Options

AI -8 ~A
B2 I - 1 15 ~A
CI - 1 8 ~A
D8 I -15 ~A

Correct answer

C. I - 1 8 ~A

Step-by-step solution

Given a non-singular matrix A satisfying (A-3I)(A-5I)=0 , expand the product: (A-3I)(A-5I)=A^2-8A+15I=0 . Since A is invertible, multiply both sides by A⁻¹ : A⁻¹(A^2-8A+15I)=A-8I+15A⁻¹=0 . Rearranging gives 15A⁻¹=8I-A . Dividing both sides by 8 yields: 15 8 A⁻¹=I- 1 8 A . This matches option C .

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