Let A=[a ij ] 2 × 2, where a ij ≠ 0 for all i, j and A²=I. Let a be the sum of all diagonal elements of A and b=|A|. Then 3 a²+4 b² is equal to:

Matrices and Determinants: JEE Main 2023 Mathematics question

JEE Main 2023 · 6 Apr, Morning shift · Q4510

JEE Main 20236 Apr, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

Let

\mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]_{2 \times 2}

, where

\mathrm{a}_{\mathrm{ij}} \neq 0

for all

\mathrm{i}, \mathrm{j}

and

\mathrm{A}^{2}=\mathrm{I}

. Let a be the sum of all diagonal elements of

\mathrm{A}

and

\mathrm{b}=|\mathrm{A}|

. Then

3 a^{2}+4 b^{2}

is equal to :