Inverse MA265F11Walther - Rhea

Inverse of a Matrix

Definition: Let A be a square matrix of order n x n(square matrix). If there exists a matrix B such that

A B = I n = B A

Then B is called the inverse matrix of A.

Conditions

A n x n is invertible (non-singular) if: 

• Ax=0 has a unique solution
• There is a B matrix such that A B = In
• Ax=b has a unique solution for any b---x=A^-1 b

Properties

• (AB)^-1 = B ⁻ 1

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