What is the meaning of subtracting from the identity matrix? If I subtract the matrix $A$ from the identity matrix $I$, $I - A$, is there a meaning to the resulting matrix perhaps given some conditions like invertibility or symmetry? For example,
$$
\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}
- \begin{bmatrix} a & b \\ c & d \end{bmatrix}
= \begin{bmatrix} 1-a & -b \\ -c & 1-d \end{bmatrix}
$$
For future reference, is there a good reference to lookup answers to such questions when I can't derive the answer on my own?

The difference $I - A$ is sometimes used with respect to projection matrices, where $A$ is the projection onto a subspace and $I - A$ is the projection onto the orthogonal complement of that subspace.
