**Inverse** of a **matrix**. The **inverse** of a **matrix** A is denoted as A-1, where A-1 is the **inverse** of A if the following is true: A×A-1 = A-1 ×A = I, where I is the identity **matrix**. Identity **matrix**: The identity **matrix** is a square **matrix** with "1" across its diagonal, and "0" everywhere else. The identity **matrix** is the **matrix** equivalent of the number "1.". **Matrix Calculator**. **Matrix Calculator** computes a number of **matrix** properties: rank, determinant, trace, transpose **matrix**, **inverse matrix** and square **matrix**. **Matrix calculator** supports **matrices** with up to 40 rows and columns. Rows of the **matrix** must end with a new line, while **matrix** elements in a row must be separated by a whitespace. **The Inverse of a Partitioned Matrix** Herman J. Bierens July 21, 2013 Consider a pair A, B of n×n **matrices**, partitioned as A = Ã A11 A12 A21 A22!,B= Ã B11 B12 B21 B22!, where A11 and B11 are k × k **matrices**. Suppose that A is nonsingular and B = A−1. In this note it will be shown how to derive the B ij’s in terms of the Aij’s, given that.

**A**⋅ A − 1 = I. where I is the identity

**matrix**, with all its elements being zero except those in the main diagonal, which are ones. The

**inverse**

**matrix**can be calculated as follows: A − 1 = 1 | A | ⋅ ( A a d j) t. Where: A − 1 →

**Inverse**

**matrix**. | A | → Determinant. A a d j → Adjoint

**matrix**.

**A**t → Transpose

**matrix**. The additive

**inverse**of 5 is -5 because 5+(-5) =0. Similarly, additive

**inverse**of -6 is 6 because -6+6=0. To find additive

**inverse**of a given

**matrix**A, we need to find a

**matrix**which when added to the given

**matrix**produces null

**matrix**or zero

**matrix**. To get additive

**inverse**of given

**matrix**, we just need to multiply each element of

**matrix**with. Description. Whether for a project, for school, or for a hobby, sometimes it is useful to be able to quickly do a

**Matrix**calculation.

**Matrix**

**Calculator**offers the ability to do the following types of calculations: Addition, Subtraction, Multiplication, Scaling, Transposing, calculation of the Determinant and

**Inverse**.