Math Problem Statement
For an involutory matrix A (elements of whose principal diagonal are not same) of order 2 × 2, the value of 3(trace (A))² + 4(det (A))² is equal to
Solution
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Math Problem Analysis
Mathematical Concepts
Matrix Algebra
Trace of a Matrix
Determinant of a Matrix
Involutory Matrices
Formulas
trace(A) = a + d
det(A) = ad - bc
A^2 = I (involutory property)
3(trace(A))² + 4(det(A))²
Theorems
Involutory Matrix Theorem
Suitable Grade Level
Undergraduate
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