Home
Class 12
MATHS
If A,B and C are square matrices of orde...

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

Text Solution

Verified by Experts

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`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A and B are two matrices of order 2 and det (A) is 3, det (B) is -1. then find the value of det (3 AB)

If A,B and C are n xx n matrices and det(A)=2,det(B)=3 and det(C)=5 then the value of the det (A^(2)BC^(-1)) is equal to

If A and B are square matrices of order 3 such that det(A)=-2 and det(B)=4, then : det(2AB)=

Let A be a square matreix of order n then det(A)=det(A^(T))

Let A and B are two square matrices of order 3 such that det. (A)=3 and det. (B)=2 , then the value of det. (("adj. "(B^(-1) A^(-1)))^(-1)) is equal to _______ .

If A is a square matrix of order 2 then det(-3A) is

If A is a square matrix of order 2, then det(-3A) is

If A is a square matrix of order 2, then det(-3A) is

If A and B are square matrices of order 2 such that det(AB) = det(BA) , then which one of the following is correct?

If A and B are square matrices of order 3 such that det.(A)=-2 and det.(B)=1, then det.(A^(-1)adjB^(-1). adj (2A^(-1)) is equal to