1 Check this question. The first answer presents a recursive formula to retrieve the inverse of a generic sum of matrices. So yours should be a special case.

The proof that your expression really is the inverse of $\;A\;$ is pretty easy. How it is derived can be done as follows without deep knowledge in matrix theory:

Product of inverse matrices $ (AB)^ {-1}$ Ask Question Asked 11 years, 10 months ago Modified 3 years, 8 months ago

Jan 25, 2024 · Given a square matrix, is the transpose of the inverse equal to the inverse of the transpose? $$ (A^{-1})^T = (A^T)^{-1} $$

Jun 4, 2015 · I have a theoretical question. Why are non-square matrices not invertible? I am running into a lot of doubts like this in my introductory study of linear algebra.

Jul 27, 2014 · Does a matrix have only one inverse matrix (like the inverse of an element in a field)? If so, does this mean that $A,B \\text{ have the same inverse matrix} \\iff A=B$?

Given are two matrices: $\\bf A, \\bf B$ We know that matrices $\\bf A \\neq \\bf B$ are invertable, symmetric, positive-definite and of full rank. Is it possible to give the formula for following s...

Mar 23, 2017 · 5 Actually, not all square matrices have inverses. Only the invertible ones do. For example, $\begin {bmatrix} 1 & 2 \\ 3 & 6 \end {bmatrix}$ does not have an inverse. And no, non …

May 24, 2015 · How is this a simplification of the lemma shown in Ken Miller 1981? Are we talking about "On the Inverse of the Sum of Matrices" or any other work? (In any case, I find this property quite …

Dec 3, 2018 · Explore related questions matrices numerical-linear-algebra matrix-decomposition See similar questions with these tags.