If A,B and C are square matrices of order n and det (A)=2, det(B)=3 and det ©=5, then find the value of 10det `(A^(3)B^(2)C^(-1)).`

Explanation

Given , `|A|=2,|B|=3 and |c|=5.`
Now, 10det `(A^(3)B^(2)C^(-1))=10xx|A^(3)B^(2)C^(1)|`
`=10xx|A^(3)|xx|B^(2)|xx|C^(-1)|=10xx|A^(3)|xx|B^(2)|xx|C|^(-1)`
`=(10xx|A^(3)|xx|B^(2)|)/(|C|)=(10xx2^(3)xx3^(2))/(5)=144`