Question

State the following statement is true or false

The statement "If $A$ is an orthogonal matrix, then $A^{\prime }=A^{-1}$" is

• A. True
• B. False

Answer 1

The correct option is A True

Orthogonal matrix is a square matrix with real entries whose columns and rows are Orthogonal unit vectors.

Which implies $A^{T}A=I$

Now multiply with $A^{-1}$ on both sides , we get $A^{T}A{A}^{-1}=I{A}^{-1}$

$\Rightarrow A^T=A^{-1}$

Therefore given statement is true