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The number of different matrices that can be formed with elements $0,1,2,3$; each matrix having $4$ elements is

  1. $2\times 4^4$
  2. $3\times 4^4$
  3. $4\times 4^4$
  4. $3\times 2^4$
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the matrices can be formed in order 4X1, 1X4 or 2X2

For each order, the number of different matrices =The number of ways to fill four places by=0,1,2,3

\Rightarrow 4 X 4 X 4 X 4 = 4^{4}

So, number of different matrices = 3 * 4^4

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