If A and B are 2×2 matrices det (A) = -5 and det (B) = -4, calculate det (3 B A B^-1)?

kb2016-10-10T08:45:31Z

Favorite Answer

det(3BAB^(-1))
= 3^2 det(BAB^(-1)), since A and B are 2 x 2 matrices
= 9 * det(B) * det(A) * det(B^(-1)), since det is multiplicative
= 9 * det(B) * det(A) * 1/det(B)
= 9 * det(A)
= 9 * (-5)
= -45.

I hope this helps!

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