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)

Answer 1

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")`.