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Q77.Let P and Q be 3 × 3 matrices with P ≠Q. If P 3 = Q3 and P 2Q = Q2P , then determinant of (P 2 + Q2) is equal to (1) −2 (2) 1 (3) 0 (4) −1

What This Question Tests

This question tests advanced matrix algebra, specifically manipulating given matrix equations to simplify expressions and then finding the determinant. It requires recognizing algebraic identities in matrix form and properties of non-singular matrices.

Concepts Tested

Matrix multiplicationDeterminant propertiesAlgebraic manipulation of matricesMatrix factorization

Formulas Used

A^3 - B^3 = (A-B)(A^2+AB+B^2)

det(AB) = det(A)det(B)

If (A-B)X = 0 and A!=B, then X is singular (det(X)=0)

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📋 Question Details

Chapter
Matrices
Topic
Matrix algebra, properties of determinants
Year
2012
Shift
Offline
Q Number
Q77
Type
MCQ
NCERT Ref
Class 12 Mathematics Ch 3: Matrices, Class 12 Mathematics Ch 4: Determinants

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