## Compute and Simplify the Matrix Expression Including Transpose and Inverse Matrices

## Problem 297

Let $A, B, C$ be the following $3\times 3$ matrices.

\[A=\begin{bmatrix}

1 & 2 & 3 \\

4 &5 &6 \\

7 & 8 & 9

\end{bmatrix}, B=\begin{bmatrix}

1 & 0 & 1 \\

0 &3 &0 \\

1 & 0 & 5

\end{bmatrix}, C=\begin{bmatrix}

-1 & 0\ & 1 \\

0 &5 &6 \\

3 & 0 & 1

\end{bmatrix}.\]
Then compute and simplify the following expression.

\[(A^{\trans}-B)^{\trans}+C(B^{-1}C)^{-1}.\]

(*The Ohio State University, Linear Algebra Midterm Exam Problem*)

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