Question

define inverse of matrix with formula​

Answer 1

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QUESTION :- explain inverse of matrix and derive the formula .

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ANSWER :- 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.

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Answer 2

The concept of inverse of a matrix is a multidimensional generalization of the concept of reciprocal of a number: the product between a number and its reciprocal is equal to 1; the product between a square matrix and its inverse is equal to the identity matrix.

Formula :-

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).