Question:

What is the total number of possible matrices of order $3 \times 3$ with each entry as $\sqrt{2}$ or $\sqrt{3}$?

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For a matrix of order $m \times n$, the number of possible matrices when each entry has $k$ choices is given by $k^{m \times n}$.
Updated On: Jun 23, 2025
  • 9
  • 512
  • 615
  • 64
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The Correct Option is B

Solution and Explanation

In a matrix of order $3 \times 3$, there are 9 entries. Each entry can either be $\sqrt{2}$ or $\sqrt{3}$, so for each entry, there are 2 possible choices. The total number of possible matrices is therefore given by: \[ 2^9 = 512 \] Thus, the total number of possible matrices is 512.
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