Talk:Transformation of Unit Matrix into Inverse

How sure are we that:
 * $\mathbf{A}=\mathbf{\breve{E}_1 \breve{E}_2 \cdots \breve{E}_{t-1} \breve{E}_t}$

implies
 * $\breve{\mathbf{A} }= \mathbf{\breve{\breve{E} }_1 \breve{\breve{E} }_2 \cdots \breve{\breve{E} }_{t-1} \breve{\breve{E} }_t}$

?

That is can we say that $\left({\mathbf A \mathbf B}\right)^{-1} = \mathbf A^{-1} \mathbf B^{-1}$? Isn't it $\left({\mathbf A \mathbf B}\right)^{-1} = \mathbf B^{-1} \mathbf A^{-1}$?

In which case your line above would be:


 * $\breve{\mathbf{A} }= \mathbf{\breve{\breve{E} }_t \breve{\breve{E} }_{t-1} \cdots \breve{\breve{E} }_2 \breve{\breve{E} }_1}$

am I right?