## Precalculus (6th Edition) Blitzer

Consider two matrices A and B. $A=\left[ {{a}_{ij}} \right]$ and $B=\left[ {{b}_{ij}} \right]$ are said to be equal if and only if both matrices have the same order and A element is equivalent to every corresponding element of B; that is, ${{a}_{ij}}={{b}_{ij}}$ for all i and j. The order of the matrix means the number of rows and columns in the matrix. Example: Consider two matrices $\left[ \begin{matrix} k & l \\ m & n \\ \end{matrix} \right]$ and $\left[ \begin{matrix} k & l \\ m & n \\ \end{matrix} \right]$ The above matrices are said to be equal as both matrices are of the order $2\times 2$ and ${{a}_{ij}}={{b}_{ij}}$ for $1\le i\le 2$, $1\le j\le 2$.