Question

The number of all possible matrices of order $3 \times 3$ with each entry $0$ or $1$ is:
E. $27$
F. $18$
G. $81$
H. $512$

Answer 1

Hint: Count the total number of places in the matrix and for each place we have two entries.
We’ll consider the matrix of order $3 \times 3$. Let the matrix be $A = \left[ {\begin{array}{*{20}{c}}
  \_&\_&\_ \\
  \_&\_&\_ \\
  \_&\_&\_
\end{array}} \right]$. Observe that we have $3 \times 3 = 9$ places in total and for each place we have $2$ entries i.e.$0$ or $1$.
Total number of possible matrices will be $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = {2^9} = 512$.

Note: We just need to think logically to solve this question. The order of the matrix could be anything and so the number of entries for each place. Infinitely many questions can be formed in this simple concept.