Given that A is of 2 times2 and det A 12 find det6ASolution

Given that A is of 2 times2 and det A = -12. find det6A.

Solution

If A is nxn matrix then det(kA) = kⁿ.det(A) where k = constant

From the given data A is 2x2 matrix

Hence ,

n = 2

det(A) = -12

det(6A) = (6)².det(A)

= (6)².(-12)

= 36.(-12)

det(6A) = -432

Therefore ,

det(6A) = -432