Let A=[ lll0 1 2 a 0 3 1 c 0 ], where a, c R. If A³=A and the positive value of a belongs to the interval (n-1, n], where n N, then n is equal to _ _ _ _ _ _.

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Morning shift · Q40

JEE Main 202311 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]

, where

a, c \in \mathbb{R}

. If

A^{3}=A

and the positive value of

a

belongs to the interval

(n-1, n]

, where

n \in \mathbb{N}

, then

n

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2023 · 11 Apr, Morning shift · Q40

JEE Main 202311 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]

, where

a, c \in \mathbb{R}

. If

A^{3}=A

and the positive value of

a

belongs to the interval

(n-1, n]

, where

n \in \mathbb{N}

, then

n

is equal to ___________.

Your answerType your answer. Integers and decimals are accepted.