Question

This is a TRUE-FALSE Question with justification.

- If Q is an orthogonal
*n×n*matrix, then Row(Q) = Col(Q).

The Answer to this is TRUE. I want to know a solid reasoning/explanation for it.

In one of the answers, it says that " Since Q is orthogonal,
Q^{T}Q = I, so Q is invertible, hence Row(Q) = Col(Q) =
R^{n}. But my question is: Why is it that for an invertible
matrix, Row(Q) = Col (Q) ?

Any other explanation that is understandable will also help.

Thanks.

Answer #1

^{n} is
R^{n}. As space is a subspace of R^{n} (as
the vectors are independent) and having dimension n.

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