Answer
(a) the statement is true
(b) the statement is false
(c) the statement is true
Work Step by Step
(a) the statement is true because
$BA=CA$ and $A$ is invertible, then
$(BA)A^{-1}=(CA)A^{-1}$ thus
$B(AA^{-1})=C(AA^{-1})$ and then
$BI=CI$ Thus
$B=C$
(b) the statement is false because
Let the product $AB$ is invertible , then $(AB)^{-1}(AB)=I$
$(AB)^{-1}(AB)B^{-1}=IB^{-1}=B^{-1}$
so we have that $(AB)^{-1}AI=B^{-1}$
$(AB)^{-1}A=B^{-1}$ IMPLIES $(AB)^{-1}AA^{-1}=B^{-1}A^{-1}$ Thus
$(AB)^{-1}I=B^{-1}A^{-1}$ Thus $(AB)^{-1}=B^{-1}A^{-1}$
(c) the statement is true because the identity matrix is nonsingular
