Use the fact that if , then to find the inverse of each matrix, if possible. Check that $A{A}^{-1}=I_2$ and $A^{-1}A=I_2$.
$A = \(\begin{bmatrix}\)3 & -1 \\-4 & 2\(\end{bmatrix}\)$

Write each matrix equation as a system of linear equations without matrices.

$\(\begin{bmatrix}\)4 & -7 \\2 & -3\(\end{bmatrix}\[\begin{bmatrix}\)x \\(\y\]\end{bmatrix}\)=\(\begin{bmatrix}\)-3 \\1\(\end{bmatrix}\)$

Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.

$\(\begin{cases}\)x + 3y + 4z = -3 \\(\x\) + 2y + 3z = -2 \\(\x\) + 4y + 3z = -6\(\end{cases}\)$

Write each linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.

$\(\begin{cases}\)6x + 5y = 13 \\5x + 4y = 10\(\end{cases}\)$

Use the fact that if , then to find the inverse of each matrix, if possible. Check that $A{A}^{-1}=I_2$ and $A^{-1}A=I_2$.

$A = \(\begin{bmatrix}\)10 & -2 \\-5 & 1\(\end{bmatrix}\)$

Use the fact that if , then to find the inverse of each matrix, if possible. Check that $A{A}^{-1}=I_2$ and $A^{-1}A=I_2$.

In Exercises 43–44, (a) Write each linear system as a matrix equation in the form AX = B (b) Solve the system using the inverse that is given for the coefficient matrix.

In Exercises 39–42, find A^(-1) Check that AA^-1 = I and A^(-1)A = I

In Exercises 37–38, find the products and to determine whether B is the multiplicative inverse of A.