Square matrix 2x2 how many can be formed using only 0,1,2?

Question

How can i find out how many square matrices can be found using only 0,1 and 2. Does there exist a formula for find such for larger square matrices

Answer 1

You have 4 entries in the matrix. For every entry there are 3 options, so $3^4$.

Answer 2

In a $2 \times 2$ matrix, you have places to fill these given numbers. Since you have been given 3 numbers: 0,1,2. So each place can take any of these 3 values as there is no other condition given. So, you have 3 options for 4 places. So total posibilities = $3^4$.

Answer 3

Guide:

• How many entries are there for a $2 \times 2$ matrix? Suppose your answer is $x$.

• At each of the location, you have $3$ options. Hence the solution is $3^x$.

You should be able to generalize it for larger matrices, $m$ choices and even address non-square arrays.