Question

vi) Which is the required factor to find the multiplicative inverse of a
matrix:
A) Determinant B) Product of elements
C) Sum of elements D) Order

Answer 1

Given :   a matrix:

To Find :   Which is the required factor to find the multiplicative inverse of a

matrix:  

A) Determinant B) Product of elements  

C) Sum of elements D) Order  

Solution:

multiplicative inverse of a matrix Exist if and only if determinant of matrix is  non zero

Hence required factor to find the multiplicative inverse of a matrix  is

Determinant

Let say matrix A

A⁻¹  =  Adj A /| A|  

| A|    = Determinant of matrix

Adj A = Adjoint matrix

AA⁻¹  = I

Then A⁻¹  is   multiplicative inverse of   matrix

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Answer 2

Step-by-step explanation:

Given:

Which is the required factor to find the multiplicative inverse of a

matrix:

A) Determinant B) Product of elements

C) Sum of elements D) Order

Solution:

We know that multiplicative inverse of a matrix is given by

$AA^{-1}=I$

Thus to find multiplicative inverse of a matrix it's inverse should exists.

Inverse of a matrix exists only it determinant of matrix is not equal to zero.

$|A|\neq0$

Thus,

Option A is correct.

Final answer:

Determinant is the required factor to find the multiplicative inverse of a matrix.

Option A is correct.

Hope it helps you.

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