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Question
Choose the correct alternative.
If A2 + mA + nI = O and n ≠ 0, |A| ≠ 0, then A–1 = _______
Options
`(-1)/"m"("A" + "nI")`
`(-1)/"n"("A" + "mI")`
`(-1)/"n"("I" + "mA")`
(A + mnI)
Solution
A2 + mA + nI = O
∴ A–1A2 + mA–1A + n A–1 I = 0
∴ (A–1 A)A + mI + n A–1 = 0
∴ IA + mI + nA–1 = 0
∴ A–1 = `(-1)/"n"("A" + "mI")`.
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