Question

If A and B are square matrix of order 3 such that |A|= -1 and |B|= 3, then find the values of |3AB|

Answer 1

Determinant of 3AB = 3 ^n det (A) det(B), where n is the order of the matrix.

Answer 2

Answer:

The value of |3AB| is -81

Step-by-step explanation:

Given If A and B are square matrix of order 3 such that |A|= -1 and |B|= 3, then we have to find the value of  |3AB|.

As, if A is the nth order square matrix then by formula

$|kA|=k^n|A|$

Here, A and B are square matrix of order 3 i.e n=3

$|3AB|=|3A||B|=3^3|A||B|=27(-1)(3)=-81$

Hence, the value of |3AB| is -81.