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

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Correct option is B

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=0 Suppose 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 $2 \times 2$ matrix such that $A^{2}$ = O, then $t r (A)$ is