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

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 $A^{-1}A=I_2$.

$A = \(\begin{bmatrix}\)3 & -1 \\-4 & 2\(\end{bmatrix}\)$

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

Answer each question. What is the product of and I₂ (in either order)?

Answer each question. What is the product ?

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix I_n.)