The number of all possible matrices of order $3 \times 2$ with each entry 1 or 2 is :

Step 1: Understand Matrix Order and Entries

A matrix of order $3 \times 2$ has 3 rows and 2 columns. This means there are a total of $3 \times 2 = 6$ positions or entries in the matrix.

Step 2: Determine Choices for Each Entry

Each entry in the matrix can be either 1 or 2. So, for each of the 6 positions, there are 2 possible choices.

Step 3: Calculate Total Number of Matrices

Since each of the 6 entries can be chosen independently from 2 options, the total number of possible matrices is found by raising the number of choices per entry to the power of the total number of entries.

Step 4: Compute the Result

Calculating $2^6$ gives us 64. Therefore, there are 64 possible matrices of order $3 \times 2$ where each entry is either 1 or 2.

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