The given matrix A=1000−10001 is a diagonal matrix.
For a diagonal matrix, the inverse is found by taking the reciprocal of each diagonal element.
The diagonal elements of A are: 1,−1,1
Their reciprocals are:
11=1
−11=−1
11=1
Therefore:
A−1=1000−10001
Note that A−1=A, meaning A is its own inverse.