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If A is 2 × 2 matrix such that $A^{2} = O,$ then $t r (A)$ is

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Correct option is C

Let A=a bc d, then A2=a2+bc ab+bdac+cd bc+d2Now, A2=O⇒a2+bc=0, (a+d)b=0(a+d)c=0, bc+d2=0Suppose , a+d≠0, then b=0,c=0.∴a2=0,d2=0⇒a=0,d=0Contradiction. Thus, a+d=0 we get ⁡tr⁡(A)=0

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If A is 2 × 2 matrix such that A2=O, then tr(A)is

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If A is 2 × 2 matrix such that $A^{2} = O,$ then $t r (A)$ is