Identify the correct statement:

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(B) For a system of $n$ linear equations $AX = B$ to have a unique solution,the determinant of the coefficient matrix $A$ must be non-zero $(|A| 
eq

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If a system of $n$ simultaneous linear equations has a unique solution,then the coefficient matrix is non-singular.

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(B) For a system of $n$ linear equations $AX = B$ to have a unique solution,the determinant of the coefficient matrix $A$ must be non-zero $(|A| 
eq 0)$. This means the matrix $A$ is non-singular. Thus,statement $(B)$ is correct.Regarding $(A)$,it is incorrect because a unique solution requires a non-singular matrix.Regarding $(C)$,if $A^{-1}$ exists,then $|A| 
eq 0$. Since $|adj A| = |A|^{n-1}$,it follows that $|adj A| 
eq 0$,so $(adj A)^{-1}$ must exist.Regarding $(D)$,using the property of the given matrix,$F(x) \cdot F(y) = F(x + y)$,not $F(x - y)$.

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