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Class 12 Matrices · Mcq Single Correct1 Marksmatrix_polynomials_and_inverse

Class 12 Maths · Matrices · Mcq Single Correct #5

Find x+y for constants x,y such that the identity A⁻¹=xA+yI holds for every real square matrix A satisfying A²−3A+I=O.

✅ Step-by-Step Solution

Final Answer: Option (B): 2
  1. The polynomial gives A(3I−A)=I=(3I−A)A, proving invertibility and A⁻¹=−A+3I. The universal coefficients are x=−1,y=3, so x+y=2.

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