Question

The number of square matrices of order 2 using numbers 1 and -1 exactly once and the number 0 twice is:

• A. 24
• B. 09
• C. 12
• D. 6

Answer 1

The Correct Option is C

To find the number of square matrices of order 2 using the numbers 1, -1 exactly once and the number 0 twice, follow these steps:

1. We are considering matrices of the form: $\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$ where each element is from the set {1, -1, 0, 0}.
2. First, select 2 positions out of the 4 for the 0s. The number of ways to choose 2 positions out of 4 is given by $\genfrac{}{}{0ex}{}{\left(4\right)}{}$. Thus, the number of ways is: $4^2=6$.
3. Now that the remaining 2 positions must be filled with 1 and -1, there are 2 ways to arrange them in the selected positions.
4. Thus, the total number of matrices is obtained by multiplying these outcomes:

$6\times 2=12$.

Therefore, the number of such matrices is 12.