Math Problem Statement

7 Let A= [ajl22, where aj 0 for all i,j and A2 = 1. Let a be the sum of all diagonal elements of A and b = |A|. Then 3a? + 4b is equal to

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Theory
Involutory Matrices

Formulas

Trace of a matrix: tr(A) = sum of diagonal elements
Determinant of a 2x2 matrix: |A| = a_11 * a_22 - a_12 * a_21
Involutory matrix property: A^2 = I

Theorems

Involutory Matrix Theorem
Determinant Theorem

Suitable Grade Level

Undergraduate (Linear Algebra Level)