Let A be the 21 x 21 matrix whose (i, j)-entry is defined by Aij = 0 if 1 ≤i, j≤ 10 or 11 ≤ i, j≤ 21, and Aij = 1 otherwise.
1. Find the (1, 10)-entry of the matrix A².
2. Find the (11, 20)-entry of the matrix A².
3. Find the (1, 10)-entry of the matrix A^10.
4. Find the (11, 20)-entry of the matrix A^10
5. Find the (1, 20)-entry of the matrix A^10
A solution to this problem will be available after the due date.