Question

Identify each matrix A such that matrix A^2 has identical diagonal elements.

Answer 1

`\begin{pmatrix}7&1&5\\ \:1&5&7\\ \:\:5&7&1\end{pmatrix}` ,
`\begin{pmatrix}9&18&27\\ \:27&-9&18\\ \:18&27&9\end{pmatrix}`,
`\begin{pmatrix}8&1&6\\ \:\:6&8&1\\ \:\:1&6&8\end{pmatrix}`,

Explanation:

Given: matrices

To find: the matrix that has identical diagonal elements

Solution:

A matrix is a rectangular array in which elements are arranged in rows and columns. Two matrices are said to be equal if their corresponding elements are equal.

`\begin{pmatrix}7&1&5\\ \:1&5&7\\ \:5&7&1\end{pmatrix}\begin{pmatrix}7&1&5\\ \:\:1&5&7\\ \:\:5&7&1\end{pmatrix}=\begin{pmatrix}75&47&47\\ \:47&75&47\\ \:47&47&75\end{pmatrix}`

`\begin{pmatrix}7&-1&5\\ \:-\:1&7&6\\ \:\:5&4&5\end{pmatrix}\begin{pmatrix}7&-1&5\\ \:\:-\:1&7&6\\ \:\:\:5&4&5\end{pmatrix}=\begin{pmatrix}75&6&54\\ \:16&74&67\\ \:56&43&74\end{pmatrix}`

`\begin{pmatrix}7&4&6\\ \:6&4&7\\ \:4&6&7\end{pmatrix}\begin{pmatrix}7&4&6\\ \:\:6&4&7\\ \:\:4&6&7\end{pmatrix}=\begin{pmatrix}97&80&112\\ \:94&82&113\\ \:92&82&115\end{pmatrix}`

`\begin{pmatrix}9&18&27\\ \:27&-9&18\\ \:18&27&9\end{pmatrix}\begin{pmatrix}9&18&27\\ \:\:27&-9&18\\ \:\:18&27&9\end{pmatrix}=\begin{pmatrix}1053&729&810\\ \:324&1053&729\\ \:1053&324&1053\end{pmatrix}`

`\begin{pmatrix}8&1&6\\ \:\:6&8&1\\ \:\:1&6&8\end{pmatrix}\begin{pmatrix}8&1&6\\ \:\:\:6&8&1\\ \:\:\:1&6&8\end{pmatrix}=\begin{pmatrix}76&52&97\\ \:97&76&52\\ \:52&97&76\end{pmatrix}`

`\begin{pmatrix}4&5&6\\ \:6&4&-5\\ \:5&6&4\end{pmatrix}\begin{pmatrix}4&5&6\\ \:\:6&4&-5\\ \:\:5&6&4\end{pmatrix}=\begin{pmatrix}76&76&23\\ \:23&16&-4\\ \:76&73&16\end{pmatrix}`