Q. 654.5( 2 Votes )

# Write the number

Answer :

We are given with the information that,

Each element of the 2 × 2 matrix can be filled in 3 ways, either 1, 2 or 3.

We need to find the number of total 2 × 2 matrices with each entry 1, 2 or 3.

Let A be 2 × 2 matrix such that, Note that, there are 4 elements in the matrix.

So, if 1 element can be filled in 3 ways, either 1, 2 or 3.

That is,

Number of ways in which 1 element can be filled = 31

Then,

Number of ways in which 4 elements can be filled = 34

Number of ways in which 4 elements can be filled = 81

Thus, total number of 2 × 2 matrices with each entry 1, 2 or 3 is 81.

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