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A sequence is a function whose domain is
Calculate the products $A B$ and $B A$ to verify that $B$ is the inverse of $A .$$$A=\left[\begin{array}{ll}{4} & {1} \\ {7} & {2}\end{array}\right] \quad B=\left[\begin{array}{rr}{2} & {-1} \\ {-7} & {4}\end{array}\right]$$
Calculate the products $A B$ and $B A$ to verify that $B$ is the inverse of $A .$$$A=\left[\begin{array}{ll}{2} & {-3} \\ {4} & {-7}\end{array}\right] \quad B=\left[\begin{array}{ll}{\frac{7}{2}} & {-\frac{3}{2}} \\ {2} & {-1}\end{array}\right]$$
Find the inverse of the matrix and verify that $A^{-1} A=A A^{-1}=I_{2}$ and $B^{-1} B=B B^{-1}=I_{3}$$$A=\left[\begin{array}{ll}{7} & {4} \\ {3} & {2}\end{array}\right]$$
Find the inverse of the matrix.$$\begin{array}{l}{\left[\begin{array}{rr}{a} & {-a} \\ {a} & {a}\end{array}\right]} \\ {(a \neq 0)}\end{array}$$
In Exercises $1-12,$ find the determinant of the matrix.$$[4]$$
