alleryFor the matrix equation $AX=B$, if $|A|\neq 0$, the unique solution is
A$X=AB$
B$X=A^{-1}$
C$X=A^{-1}B$
D$X=BA^{-1}$
Answer & Solution
Correct answer: C. $X=A^{-1}B$
When $|A|\neq 0$, the inverse $A^{-1}$ exists.
Pre-multiplying $AX=B$ by $A^{-1}$ gives $A^{-1}AX=A^{-1}B$, so $IX=A^{-1}B$, hence $X=A^{-1}B$.
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