If A=[ 2 3 0 1 sin2x -cos2x cos2x cos4x sin4x ] and A(Adj A)=K[ 1 0 0 0 1 0 0 0 1 ] , then the value of K is

Question

If A=[ 2 3 0 1 sin2x -cos2x cos2x cos4x sin4x ] and A(Adj A)=K[ 1 0 0 0 1 0 0 0 1 ] , then the value of K is (A) 0 (B) -1 (C) 1 (D) none of these

Tardigrade Admin · Accepted Answer

A(A d j A)=|A| I3 K=|A|=2( sin 6 x+ cos 6 x)-3( sin 4 x+ cos 4 x) =2(1-3 sin 2 x ⋅ cos 2 x)-3(1-2 sin 2 x cos 2 x)=-1

Q. If $A = ⎣ ⎡ 21 co s^{2} x 3 s i n^{2} x co s^{4} x 0 - co s^{2} x s i n^{4} x ⎦ ⎤$ and $A (A d j A) = K ⎣ ⎡ 100010001 ⎦ ⎤$ , then the value of $K$ is