Let and be two square matrices of same order satisfying and respectively, where is the identity matrix. Then the inverse of the matrix is:

Explanation: Solution Step 1: Factorize Matrix Step 2: Use given equations to find individual inverses For : Add to both sides: Therefore, . For : Add to both sides: Therefore, . Step 3: Calculate Using the property : Substitute the values from Step 2: Final Answer: The inverse of matrix is . The correct option is (A) .

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NIMCET 2025 — Mathematics PYQ

NIMCET | Mathematics | 2025

Let $A$ and $B$ be two square matrices of same order satisfying $A^2+5A+5I=0$ and $B^2+3B+I=0$ respectively, where $I$ is the identity matrix. Then the inverse of the matrix $C = BA + 2B + 2A + 4I$ is:

Choose the correct answer: