From the matrix equation AB = AC we can conclude B = C provided
A is singular
A is non-singular
A is symmetric
A is square
As we have learned
Singular matrix -
- wherein
denotes determinants of
Since, |A| 0. So, A-1 exists.
AB = AC A-1(AB) = A-1(AC)
(A-1A)B = (A-1A) C B = C
Option 1)
A is singular
Option 2)
A is non-singular
Option 3)
A is symmetric
Option 4)
A is square
Study 40% syllabus and score up to 100% marks in JEE