For $A=\begin{pmatrix}1&2\ 3&4\end{pmatrix}$, Lina claims that \(A^2=\begin{pmatrix}1&4

Question

For $A=\begin{pmatrix}1&2\ 3&4\end{pmatrix}$, Lina claims that $A^2=\begin{pmatrix}1&4\ 9&16\end{pmatrix}$. Explain the error.[1] Calculate the correct $A^2$.[3]

Accepted Answer

(a) Entrywise squaring is invalid. (b) $\begin{pmatrix}7&10\ 15&22\end{pmatrix}$.

Checking a claimed matrix square

Checking a claimed matrix square

Solution:

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