The Identity Matrix

Verify that A × I = A for A = $\left(\begin{array}{cc}3& 5\\ 2& 4\end{array}\right)$.

• 1I = $\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$
• 2Top-left: ($3\times 1$) + ($5\times 0$) = $3$. Top-right: ($3\times 0$) + ($5\times 1$) = $5$
• 3Bottom-left: ($2\times 1$) + ($4\times 0$) = $2$. Bottom-right: ($2\times 0$) + ($4\times 1$) = $4$

Answer: A × I = $\left(\begin{array}{cc}3& 5\\ 2& 4\end{array}\right)$ = A ✓