College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 22

State whether the matrices $\displaystyle A = \left[ \begin{array}{cc}
\sqrt{25} & 1 \\
0 & 2^{-1}
\end{array} \right]$ and $B = \left[ \begin{array}{cc}
5 & e^0 \\
\log 1 & \displaystyle \frac{1}{2}
\end{array} \right]$ are equal.

Matrices $A$ and $B$ are equal, because when both matrices are simplified they will have the same result.

In matrix $A$

$\displaystyle A = \left[ \begin{array}{cc}
\sqrt{25} & 1 \\
0 & 2^{-1}
\end{array} \right] = \left[ \begin{array}{cc}
5 & 1 \\
0 & \displaystyle \frac{1}{2}
\end{array} \right] $

And in matrix $B$

$\displaystyle B = \left[ \begin{array}{cc}
5 & e^0 \\
\log 1 & \displaystyle \frac{1}{2}
\end{array} \right] = \left[ \begin{array}{cc}
5 & 1 \\
0 & \displaystyle \frac{1}{2}
\end{array} \right]$