Problems from Transposed matrix

If $$B^t=\left( \begin{array}{cccc} 1 & 3 & 5 & 6 \\ 0 & 1 & 0 & 2 \\ 0 & 5 & 4 & 1 \end{array} \right)$$

calculate the original matrix $$B$$.

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Development:

Now we just have to swap rows with columns again:

$$B=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 3 & 1 & 5 \\ 5 & 0 & 4 \\ 6 & 2 & 1 \end{array} \right)$$

If we now calculate the transpose of this matrix we see that it is $$B^t$$.

Solution:

$$B=\left( \begin{array}{ccc} 1 & 0 & 0 \\ 3 & 1 & 5 \\ 5 & 0 & 4 \\ 6 & 2 & 1 \end{array} \right)$$

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What is the transpose of the matrix $$A=\left( \begin{array}{ccc} 1 & 8 & 1 \\ 2 & 7 & 0 \\ 0 & 5 & 3 \end{array} \right)$$?

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Development:

Let's swap rows with columns in order:

$$A^t=\left( \begin{array}{ccc} 1 & 2 & 0 \\ 8 & 7 & 5 \\ 1 & 0 & 3 \end{array} \right)$$

Solution:

$$A^t=\left( \begin{array}{ccc} 1 & 2 & 0 \\ 8 & 7 & 5 \\ 1 & 0 & 3 \end{array} \right)$$

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