P is a 3 times 3 square matrix and operatorna | vedclass

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(B) We know that for any square matrix $P$, the trace of its transpose is equal to the trace of the matrix itself, i.e.,$\operatorname{Tr}(P) = \opera

Vedclass · Accepted Answer

$-1$

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(B) We know that for any square matrix $P$, the trace of its transpose is equal to the trace of the matrix itself, i.e.,$\operatorname{Tr}(P) = \operatorname{Tr}(P^T)$.Also, $\operatorname{Tr}(P - P^T) = \operatorname{Tr}(P) - \operatorname{Tr}(P^T) = 0$ and $\operatorname{Tr}(P + P^T) = \operatorname{Tr}(P) + \operatorname{Tr}(P^T) = 2\operatorname{Tr}(P)$.Substituting these into the given equation:$0 + 2\operatorname{Tr}(P) + \frac{\operatorname{Tr}(P)}{\operatorname{Tr}(P)} + \operatorname{Tr}(P) 	imes \operatorname{Tr}(P) = 0$Since $\operatorname{Tr}(P) 
eq 0$, we have $\frac{\operatorname{Tr}(P)}{\operatorname{Tr}(P)} = 1$.Thus, the equation becomes: $2\operatorname{Tr}(P) + 1 + (\operatorname{Tr}(P))^2 = 0$.This is a quadratic equation in terms of $\operatorname{Tr}(P)$:$(\operatorname{Tr}(P))^2 + 2\operatorname{Tr}(P) + 1 = 0$$(\operatorname{Tr}(P) + 1)^2 = 0$$\operatorname{Tr}(P) = -1$.

$P$ is a $3 \times 3$ square matrix and $\operatorname{Tr}(P) \neq 0$. If $\operatorname{Tr}(P-P^{T})+\operatorname{Tr}(P+P^{T})+\frac{\operatorname{Tr}(P)}{\operatorname{Tr}(P^T)}+\operatorname{Tr}(P) \times \operatorname{Tr}(P^{T})=0$, then $\operatorname{Tr}(P)=$

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