If det A 2 for some 5 times 5 mztrix A what is det 2 AT ASo

If det (A) = -2 for some 5 times 5 mztrix A, what is det (-2 A^T A)?

Solution

Given ---------------Det(A)=-2

To Find--------------Det(-2A^tA)

Solution:- We know that--(underlined Indentity)

Det(A^t)=Det(A)

Det(Aⁿ) = Det(A)ⁿ

Det(KA)= Kⁿ Det(A)

Det(KA^T A)=Det(A)²Kⁿ

^{Where n=5 and k=-2 Det(A)= -2}

Det(-2A^tA)=(-2)⁵ (-2)²
Det(-2A^tA)=(-2)⁷
Det(-2A^tA)= -128--------------------------------------------Answer