Respuesta :
Answer:
[tex]A^{-1} = \left[\begin{array}{cccc}0&0&0&1\\0&0&1&0\\1&0&0&0\\0&1&0&0\end{array}\right][/tex]
Step-by-step explanation:
As provided A square matrix is named a permutation matrix if it includes input 1 precisely once for each row and columns with 0 in all the other entries.
And then all matrix with permutation are invertible.
We've got matrix A, by,
[tex]\left[\begin{array}{cccc}0&0&1&0\\0&0&0&1\\0&1&0&0\\1&0&0&0\end{array}\right][/tex]
Matrix A includes the entry 1 precisely once for each row and other such entries for each column were also 0.
So that we could say matrix A is matrix permutation.
We understand that the inverse matrix is equivalent to the matrix transposition.
So we could be saying that
[tex]A^{-1} = A^T[/tex] ........................ (1)
To get AT from matrix A consider writing the matrix A column row as AT column
The first row becomes first column, the second row became a second column and the third row has become the third column.
we have,
[tex]A^T = \left[\begin{array}{cccc}0&0&0&1\\0&0&1&0\\1&0&0&0\\0&1&0&0\end{array}\right][/tex]
We can say that from equation 1 that
[tex]A^{-1} = \left[\begin{array}{cccc}0&0&0&1\\0&0&1&0\\1&0&0&0\\0&1&0&0\end{array}\right][/tex]
