From the matrix equation AB = AC we can conclude B = C provided

  • Option 1)

    A is singular 

  • Option 2)

    A is non-singular

  • Option 3)

    A is symmetric 

  • Option 4)

    A is square

 

Answers (1)
G gaurav

As we have learned

Singular matrix -

\left | A \right |=0 

- wherein

\left | A \right | denotes determinants of A

 

 

            Since, |A| \neq  0. So, A-1 exists.

                              \therefore AB = AC \Rightarrow A-1(AB) = A-1(AC)

                 \Rightarrow (A-1A)B = (A-1A) C    \Rightarrow B = C

           

 


Option 1)

A is singular 

Option 2)

A is non-singular

Option 3)

A is symmetric 

Option 4)

A is square

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