Question

To find the inverse of a matrix, which amongst the following are required?

Answer 1

Answer:To find the inverse of a square matrix A , you need to find a matrix A−1 such that the product of A and A−1 is the identity matrix. In other words, for every square matrix A which is nonsingular there exist an inverse matrix, with the property that, AA−1=A−1A=I , where I is the identity matrix of the appropriate size.

Step-by-step explanation:

Answer 2

Given : To find  inverse of a matrix

To Find : which amongst the following are required

Select one:

a. all of these

b. cofactors

c. minors

d. determinant

Solution:

all of these is correct answer

if matrix A

then A⁻¹  = adj A / | A |

| A | = determinant of matrix  

if  | A | = 0 then inverse  of matrix does not exist.

adj A is adjoint of matrix

Minors and cofactors  are used to find   adjoint of matrix  

Cij  = (-1)^(i + j) Mij

Cij = Cofactor of element ij

Mij = Minor of element ij

b. cofactors

c. minors

d. determinant

all required to find inverse of matrix

Hence al of the these are required to find inverse of a matrix

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