Let M = \ A = (a b c d):a,b,c,d ± 3, ± 2, ± 1,0 \. Define f: M → Z, as f(A) = det(A), for all A M, where z is set of all integers. Then the number of A M such that f(A) = 15 is equal to _ _ _ _ _ _ _.

Matrices and Determinants: JEE Main 2021 Mathematics question

JEE Main 2021 · 25 Jul, Morning shift · Q37

JEE Main 202125 Jul, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

M = \left\{ {A = \left( {\matrix{ a & b \cr c & d \cr } } \right):a,b,c,d \in \{ \pm 3, \pm 2, \pm 1,0\} } \right\}

. Define f : M

\to

Z, as f(A) = det(A), for all A

\in

M, where z is set of all integers. Then the number of A

\in

M such that f(A) = 15 is equal to _____________.

Your answerType your answer. Integers and decimals are accepted.