Matrices and Transpose

Question

Proposition. If $c$ is a number, show that $^{t}\left( cA\right) =c^{t}A.$

My question is that what is $c^{t}$ mean/say? Can you give example about $c$ and $c^{t}$?

Answer 1

In your notation it looks like the superscript "$^t$" precedes the object that it applies to. So, using parentheses to make it explicit, you want to show $$^t(cA) = c( ^tA)$$ In words, "the transpose of ($c$ times $A$) is $c$ times (the transpose of $A$)".