## College Algebra (6th Edition)

B is the multiplicative inverse of A. $(B=A^{-1})$
(See p.629) Let A be an n\times n square matrix. If there is a square matrix $A^{-1}$ such that $AA^{-1}=I_{n}$ and $A^{-1}A=I_{n},$ then $A^{-1}$ is the multiplicative inverse of $A$. -------------- $AB=\left[\begin{array}{ll} 4(4)+(-3)(5) & 4(3)+(-3)(4)\\ (-5)(4)+4(5) & -5(3)+4(4) \end{array}\right]=\left[\begin{array}{ll} 1 & 0\\ 0 & 1 \end{array}\right]$ $BA=\left[\begin{array}{ll} 4(4)+3(-5) & 4(-3)+3(4)\\ 5(4)+4(-5) & 5(-3)+4(4) \end{array}\right]=\left[\begin{array}{ll} 1 & 0\\ 0 & 1 \end{array}\right]$ $AB=BA=I_{2},$ so B is the multiplicative inverse of A. $(B=A^{-1})$