Question

What is necessary and sufficient condition that to have an inverse of a matrix?

Answer 1

Answer:

Definition of an Inverse of a Matrix

- Web Formulas Definition of an Inverse of a Matrix. Assuming that we have a square matrix A, which is non-singular (i.e. det (A) does not equal zero), then there exists an n × n matrix A-1 which is called the inverse of A such that: AA-1 = A-1A = I, where I is the identity matrix.

Answer 2

Step-by-step explanation:

The inverse of A is A-1 only when A × A-1 = A-1 × A = I. To find the inverse of a 2x2 matrix: swap the positions of a and d, put negatives in front of b and c, and divide everything by the determinant (ad-bc).

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