If P is a non-singular matrix of order 5 time | vedclass

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(B) Let $X$ be a column vector of order $5 	imes 1$ where all elements are $1$, i.e.,$X = [1, 1, 1, 1, 1]^T$. Given that the sum of the elements of e

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$1$

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(B) Let $X$ be a column vector of order $5 	imes 1$ where all elements are $1$, i.e.,$X = [1, 1, 1, 1, 1]^T$. Given that the sum of the elements of each row of $P$ is $1$, we can write this as $PX = X$. Since $P$ is a non-singular matrix, $P^{-1}$ exists. Multiplying both sides by $P^{-1}$, we get $P^{-1}(PX) = P^{-1}X$. This simplifies to $(P^{-1}P)X = P^{-1}X$, which is $IX = P^{-1}X$. Thus, $P^{-1}X = X$. This implies that the sum of the elements of each row of $P^{-1}$ is also $1$.

If $P$ is a non-singular matrix of order $5 \times 5$ and the sum of the elements of each row is $1$, then the sum of the elements of each row in $P^{-1}$ is

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