# 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

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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