What is the number of different matrices, each having 4 entries that can be formed using 1, 2, 3, 4 (repetition is allowed)?

Explanation

A matrix with 4 entries can have orders 1 \times 4, 4 \times 1, or 2 \times 2 (3 possible dimensions). For each dimension, each of the 4 entries can be chosen from \{1, 2, 3, 4\} in 4 ways. Number of matrices of one dimension = 4^4 = 256. Total matrices = 3 \times 256 = 768.

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