Question

what is inverse of matrix​

Answer 1

The Inverse of a Matrix is the same idea but we write it A-1

Reciprocal of A is A-inverse and back again

Why not 1/A ? Because we don't divide by a matrix! And anyway 1/8 can also be written 8-1

And there are other similarities:

When we multiply a number by its reciprocal we get 1

8 × (1/8) = 1

When we multiply a matrix by its inverse we get the Identity Matrix (which is like "1" for matrices):

A × A-1 = I

Same thing when the inverse comes first:

(1/8) × 8 = 1

A-1 × A = I

Answer 2

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. The inverse of a 2×2 matrix.