If A is an invertible matrix of order 3, then which of the following is not true
(a) $|\operatorname{adj} A|=|A|^{2}$
(b) $\left(A^{-1}\right)^{-1}=A$
(c) If $B A=C A$, than $B \neq C$, where $B$ and $C$ are square matrices of order 3
(d) $(A B)^{-1}=B^{-1} A^{-1}$, where $B \neq\left[b_{i j}\right]_{3 \times 3}$ and $|B| \neq 0$
(c) If $B A=C A$, then $B \neq C$ where $B$ and $C$ are square matrices of order 3 .
If $\mathrm{A}$ is an invertible matrix, then $A^{-1}$ exists.
Now,
$B A=C A$
On multiplying both sides by $A^{-1}$, we get
$B A A^{-1}=C A A^{-1}$
$\Rightarrow B I=C I \quad\left[\because A A^{-1}=I\right.$ where $I$ is the identity matrix $]$
$\Rightarrow B=C$
Therefore, the statement given in (c) is not true.
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