Matrices · Class 12 · CBSE · Science Mathematics
Let A be an invertible square matrix and let I be the identity matrix of the same order. If A² − 5A + 6I = O, where O is the zero matrix, then which…
Practice question from Matrices (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
hard · MCQ · Q-8E979B
Let A be an invertible square matrix and let I be the identity matrix of the same order. If A² − 5A + 6I = O, where O is the zero matrix, then which expression represents A⁻¹?
- A.(A − 5I)/6
- B.(5I − A)/6Correct answer
- C.(A − 6I)/5
- D.(6I − A)/5
Solution
From A² − 5A + 6I = O, we get A(5I − A) = 6I. Multiplying by 1/6 gives A((5I − A)/6) = I, so A⁻¹ = (5I − A)/6.
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