Question

Every Identity matrix is an orthogonal matrix.

(a) True

(b) False

This question was posed to me in unit test.

My doubt stems from Real Matrices: Symmetric, Skew-symmetric, Orthogonal Quadratic Form topic in section Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

Right option is (b) False

Easy explanation: An orthogonal matrix can be defined as ‘a matrix having its entries as orthogonal unit vectors’ or it can also be defined as ‘a matrix whose transpose is equal to its inverse’. Since this property is satisfied by an identity matrix, every identity matrix is an orthogonal matrix.