Question

Every orthogonal matrix is diagonalizable. O True O False

Answer 1

Answer:

FALSE

Step-by-step explanation:

the correct answer is FALSE

A matrix is said to be orthogonal when it is  multiplied by its own transpose then the matrix comes out to be Identity.

                                      $A^T.A = I$

the basic condition for a matrix to be diagonalizable is that the matrix should be symmetric.

but an orthogonal matrix is not necessarily symmetric so, the statement is false.