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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