Question

If A is a square matrix, then show that
(a) (A + AT
) is symmetric matrix.
(b) (A- A' )is skew symmetric
(c) (AAT
) is symmetric matrix.
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Answer 1

Answer:

Think about it, for example, let A be a 2×2 square matrix, then A=(acbd), therefore AT=(abcd)

∴A+AT=(2ab+cb+c2d) and A−AT=(c−bb−c)

You can apply the same rule to any n×n square matrices

Answer 2

Answer:

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