Let A be the set of all 3 times 3 matrices wi | vedclass

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(C) Let $M$ be a matrix in $A$. The determinant of $M$,denoted by $\det(M)$,can only take values from the set $\{ -1, 0, 1 \}$ because the entries are

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$B$ and $C$ contain the same number of elements

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(C) Let $M$ be a matrix in $A$. The determinant of $M$,denoted by $\det(M)$,can only take values from the set $\{ -1, 0, 1 \}$ because the entries are $0$ or $1$. Consider the operation of swapping two rows of a matrix $M$. Let $M'$ be the matrix obtained by swapping two rows of $M$. Then $\det(M') = -\det(M)$. If we swap two rows of a matrix $M \in B$,we get a matrix $M' \in C$ because $\det(M') = -\det(M) = -1$. Similarly,if we swap two rows of a matrix $M \in C$,we get a matrix $M' \in B$ because $\det(M') = -\det(M) = -(-1) = 1$. This defines a bijection between the sets $B$ and $C$. Therefore,the number of elements in $B$ is equal to the number of elements in $C$.

Let $A$ be the set of all $3 \times 3$ matrices with entries $0$ or $1$ only. Let $B$ be the subset of $A$ consisting of all matrices with determinant value $1$. Let $C$ be the subset of $A$ consisting of all matrices with determinant value $-1$. Then:

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Let $A = [a_{ij}]$ be a $3 \times 3$ matrix,where
$a_{ij} = 1$,if $i = j$
$a_{ij} = -x$,if $|i - j| = 1$
$a_{ij} = 2x + 1$,otherwise
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