Find the inverse of the matrix :
We can solve for using Gaussian elimination on the augmented matrix to get :
So,
Let be the matrix with all zero entries.
Yes, there are many examples. These matrices are called nilpotent matrices. For example,
Yes, there are many examples. These matrices are called idempotent matrices. For example,
Find the inverse of the matrix :
is a matrix, so we can just use the formula for the inverse.