Let A and B be two square matrices of order 2. If det (A) = 2, det (B) = 3 and det ((det 5(det A)B)A²) = 2^(a) 3^(b) 5^(c) for some a, b, c, N, then a + b + c is equal to:

Matrices and Determinants: JEE Main 2022 Mathematics question

JEE Main 2022 · 30 Jun, Morning shift · Q4533

JEE Main 202230 Jun, Morning shiftMathematicsHardMatrices and Determinants245× since 2002

Let A and B be two square matrices of order 2. If

det\,(A) = 2

det\,(B) = 3

and

\det \left( {(\det \,5(det\,A)B){A^2}} \right) = {2^a}{3^b}{5^c}

for some a, b, c,

\in

N, then a + b + c is equal to :

JEE Main 2022 · 30 Jun, Morning shift · Q4533

JEE Main 202230 Jun, Morning shiftMathematicsHardMatrices and Determinants245× since 2002

Let A and B be two square matrices of order 2. If

det\,(A) = 2

det\,(B) = 3

and

\det \left( {(\det \,5(det\,A)B){A^2}} \right) = {2^a}{3^b}{5^c}

for some a, b, c,

\in

N, then a + b + c is equal to :