If A,B and C arae three non-singular square matrices of order 3 satisfying the equation `A^(2)=A^(-1)` let `B=A^(8) and C=A^(2)` ,find the value of det (B-C)

Explanation

`therefore " " B=A^(8)=(A^(2))^(4)=(A^(1))^(4)`
`=(A^(4))^(-1)=(A^(2.2))^(-1)`
`=((A^(2))^2)^(-1)=((A^(2))^(-1))^(2)`
`=((A^(-1))^1)^(2)=A^(2)=C`
`So, " " B=C rArrB-C=0`
`therefore" "det(B-C)=0`