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2. Let A be a 3 x 3 matrix such that det(A)= -4. Find det(3A)

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Answer:

The value of det (3A) is -108.

Explanation:

If M is square matrix of order n x n, then


|kA|=k^n|A|

Let as consider a matrix A or order 3 x 3. Using the above mentioned property of determinant we get


|kA|=k^3|A|

We need to find the value of det(3A).


|3A|=3^3|A|


|3A|=27|A|

It is given that the det(A)= -4. Substitute |A|=-4 in the above equation.


|3A|=27(-4)


|3A|=-108

Therefore the value of det (3A) is -108.

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