Find det(-2A) if A is a 3x3 matrix and det(A) = -1?

Question

Find det(-2A) if A is a 3x3 matrix and det(A) = -1?

Answer 1

Recall that if A is a n x n matrix and c is a scalar, then:

det(cA) = c^n * det(A).



Therefore, since A is a 3 x 3 matrix:

det(-2A) = (-2)^3 * det(A)

= -8det(A)

= -8(-1), since det(A) = -1

= 8.



I hope this helps!

Answer 2

Use the following formula for multiplying determinants of matrices:



det(B*A) = det(B) * det(A) -- (1)



In this case, we can think of -2*A as the product of A and (-2) times the identity matrix:



-2A = (-2*I)*A.



We know det(A) = -1. Since I is a 3x3 matrix,



det(-2*I) =

det(



-2 0 0

0 -2 0

0 0 -2



)



= (-2)*(-2)*(-2) = -8.



Finally, we use formula (1) to deduce det(-2*A) = (-8)*(-1) = 8.



Good luck!



Best wishes,

Kylash

Answer 3

2

Answer 4

Since A is 3 x 3,

det(-2A) = (-2)^3 * det(A) = -8 * -1 = 8.



I hope this helps!