The number of square matrices of order 5 with entries from the set...

Given,A $5 \times 5$ matrix whose each entry is either $0 or 1$, is such that sum of entries of each column as well as each row is $1$,Taking a possible case we get,\left[$\begin{cases}1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1\end{cases}$\right]Now arranging the above case we get,\left[\begin{cases}1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1\end{cases}\right]\left($\begin{array}{ll}\to 5 \text{ways} \\ \to 4 \text{ways} \\ \to 3 \text{ways} \\ \to 2 \text{ways} \\ \to 1 \text{way}\end{array}$$because if we fix$1$at first row and first column then in second row first column$1$cannot come and vice-versa.So total number of such matrices will be$5 \times 4 \times 3 \times 2 \times 1 = 120