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Show that the matrix B'AB is symmetric o...

Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.

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To show that the matrix \( B'AB \) is symmetric or skew-symmetric according to whether \( A \) is symmetric or skew-symmetric, we will proceed with the following steps: ### Step 1: Definitions First, we need to recall the definitions of symmetric and skew-symmetric matrices: - A matrix \( A \) is **symmetric** if \( A^T = A \). - A matrix \( A \) is **skew-symmetric** if \( A^T = -A \). ### Step 2: Consider the case when \( A \) is symmetric ...
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