10.7 Homework: the identity and inverse matrices

Matrix $A$ is $\left[\begin{array}{cc}4& \text{10}\\ 2& 6\end{array}\right]$ .

• A

  Write the identity matrix $I$ for Matrix $A$ .

• B

  Show that it works.

• C

  Find the inverse matrix $A^{-1}$ .

• D

  Show that it works.

Matrix $B$ is $\left[\begin{array}{cc}1& 2\\ 3& 4\\ 5& 6\end{array}\right]$ .

• A

  Can you find a matrix that satisfies the equation $\mathrm{BI}=B$ ?

• B

  Is this an identity matrix for $B$ ? If so, demonstrate. If not, why not?

Matrix $C$ is $\left[\begin{array}{cccc}1& 2& 3& 4\\ 5& 6& 7& 8\\ 9& \text{10}& \text{11}& \text{12}\\ \text{13}& \text{14}& \text{15}& \text{16}\end{array}\right]$ . Write the identity matrix for $C$ .

Matrix $D$ is $\left[\begin{array}{cc}1& 2\\ 3& n\end{array}\right]$ .

• A

  Find the inverse matrix $D^{-1}$

• B

  Test it.