A square matrix is called a permutation matrix if it contains the entry 1 exactly once in each row and in each column, with all other entries being 0. All permutation matrices are invertible. Find the inverse of the following permutation matrix. A = [0 0 1 0, 0 0 0 1, 0 1 0 0, 1 0 0 0]

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,

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

........................ (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,

We can say that from equation 1 that