## Precalculus (6th Edition) Blitzer

Consider the two matrices $A$ and $B$ to be the multiplicative inverses; that is, the product of the matrix $AB$ is equal to the identity matrix. As example: Let matrix $A=\left[ \begin{matrix} 4 & -3 \\ -5 & 4 \\ \end{matrix} \right]$ and $B=\left[ \begin{matrix} 4 & 3 \\ 5 & 4 \\ \end{matrix} \right]$. If $B$ is the multiplicative inverse of $A$, then $AB$ will result in the identity matrix ${{I}_{2}}=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]$ And, if a square matrix does not have a multiplicative inverse, it is called singular.