Option C can never be true rank (A*B) = min {r(A),r(B)} so rank (A*A) = r(A)
Option A is true suppose A2 = A now A3 = A2*A = A*A =A2
and given A3 is 0 this implies A2 is also zero this contradicts statement given in question A2 not eqal to zero so our assumption A2 = A is wrong . this implies A2 is not equal to A For other options i dont have exact answer :)
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