Question

Help please.

Let A and B be invertible matrices. Is it true that A + B is also invertible? Illustrate your conclusion with appropriate examples.

Answer 1

no i don't think thats true a+b= you can't find the answer unless if its a=4 and b=5 that will equal to 4+5= 9

Answer 2

FALSE
consider these two matrics, they are both inverible since their determinants do not equal zero\[A =\left[\begin{matrix}1 & 0 \\ 0 & 1\end{matrix}\right], B=\left[\begin{matrix}0 & 1 \\ 1 & 0\end{matrix}\right]\]
But \[A+B = \left[\begin{matrix}1 & 1 \\ 1 & 1\end{matrix}\right]\]
det(A+B) =0 thus is not invertible