A square matrix A is said to be orthogonal if `A^T A=I` If A is a sqaure matrix of order n and k is
Channel: Doubtnut
Date: 2020-04-12

A square matrix A is said to be orthogonal if `A^T A=I` If A is a sqaure matrix of order n and k is a scalar, then `|kA|=K^n |A| Also |A^T|=|A|` and for any two square matrix A d B of same order `\AB|=|A||B|` On the basis of abov einformation answer the following question: If A is an orthogonal matrix then (A) `A^T` is an orthogonal matrix but `A^-1` is not an orthogonal matrix (B) `A^T` is not an orthogonal mastrix but `A^-1` is an orthogonal matrix (C) Neither `A^T` nor `A^-1` is an orthogonal matrix (D) Both `A^T and A^-1` are orthogonal matices.