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Let $A = (\begin{array}{ll} a ââââ b \\ c ââââ d \end{array})$ be such that $A^{3} = O$ but $A â O$ , then

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A2=O

A2 = A

A2 = I â A

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Correct option is A

As A3=O, we get A3=0|A|3=0â|A|âadâbc=0Also, A2=a2+bc(a+d)b(a+d)cbc+d2=a2+ad(a+d)b(a+d)cad+d2=(a+d)AIf a+d=0 we get A2=O.Suppose a+dâ 0, then A3=A2A=(a+d)A2â O=(a+d)A2âA2=O

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Let A=aâ â â â bcâ â â â d be such that A3=O but Aâ O, then

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Let $A = (\begin{array}{ll} a ââââ b \\ c ââââ d \end{array})$ be such that $A^{3} = O$ but $A â O$ , then