Let A be a square matrix of order 3 such that det (A)=-2 and det (3 adj (-6 adj (3 A)))=2^ m + n 3^ mn , m n . Then 4 ~m +2 n is equal to _______

Step-by-step solution

aligned & As A adj A=|A| l, det ( A)= ^n det A & det (3 adj (-6 adj (3 A)))=3^3 det ( adj (-6 adj (3 A))) & =3^3(-6 adj (3 A))^2 & =3^3(-6)^6|3 A|^4 & =3^9 2^6 3¹² (-2)^4 & =3²¹ 2¹⁰ aligned Now comparing with given condition aligned & 2^ m+n 3^ m n =2¹⁰ 3²¹ & m+n=10, m n=21 & m=7, n=3(m>n) & 4 m+2 n=28+6=34 aligned