Let the determinant of a square matrix A of order m be m-n, where m and n satisfy 4 m+n=22 and 17 m+4 n=93. If det(n adj(adj(m A)))=3^(a) 5^(b) 6^(c) then a+b+c is equal to:

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 15 Apr, Morning shift · Q4543

JEE Main 202315 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let the determinant of a square matrix A of order

m

m-n

, where

m

and

n

satisfy

4 m+n=22

and

17 m+4 n=93

. If

\operatorname{det}(n \operatorname{adj}(\operatorname{adj}(m A)))=3^{a} 5^{b} 6^{c}

then

a+b+c

is equal to :