The no. of all possible matrices of order $3\times 3$ with each entry $0$ and $1$ and $ -1$.
Finding the no. of possible matrices given the order and limited no. of entries
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matrices
permutations
2 Answers
9
Given $n\times n$ matrix with restricted $m$ elements, then number of possible matrices is $$m^{(n^2)}$$ because there are $n^2$ places to fill with $m$ choices.
In this case both $n=m=3$, therefore $3^9$ matrices.
6
There are $9$ entries in the matrix and there are $3$ choices for each entry. We get to choose whether it takes value $0$, $1$ or $-1$ independently.
Hence number of possible matrices $=3^{9}$.