Q.For the matrices $A$ and $B$ of Q1, verify that $A+B=B+A$.

[!TLDR] Compute $B+A$ entrywise and compare with $A+B$ from Q1. [!ANSWER] $B+A=\begin{bmatrix}3&3\-2&8 …

$B+A=\begin{bmatrix}1+2&4+(-1)\\-2+0&5+3\end{bmatrix}=\begin{bmatrix}3&3\\-2&8\end{bmatrix}$. This is identical, entry for entry, to $A+B=\begin{bmatrix}3&3\\-2&8\end{bmatrix}$ found in Q1. Since ordinary addition of real numbers is commutative ($a+b=b+a$ for every entry), and matrix addition is defined entrywise, matrix a …

Compute $B+A$ independently, entrywise, and compare directly with the already-computed $A+B$; note that commutativity of matrix addition follows direct …

Since addition really is commutative here, the main risk is an arithmetic slip in recomputing $B+A$ that makes it …