If is an non-singular matrix, such that ( denotes the transpose of ). Let where denotes the inverse of . Then is equal to
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DSE 2016 Question 14: Matrices, determinants and linear systems
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If X is an n× n non-singular matrix, such that XXᵀ=XᵀX (Xᵀ denotes the transpose of X). Let Y=X⁻¹Xᵀ where X⁻¹ denotes the inverse of X. Then YYᵀ is equal to (A) I+Y (I is the identity matrix) (B) I (C) Y⁻¹ (D) Yᵀ
Also written as: If X is an n* n non-singular matrix, such that XX^T=X^TX (X^T denotes the transpose of X). Let Y=X^(-1)X^T where X^(-1) denotes the inverse of X. Then YY^T is equal to
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What this question tests
This question is on Matrix identities and Cayley-Hamilton, part of Matrices, determinants and linear systems in Mathematics.
Algebraic results about matrix powers, polynomials and special classes.
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