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Question
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
Options
Diagonal matrix
Symmetric matrix
Skew-symmetric matrix
Scalar matrix
Solution
The matrix `[(0, -5,8),(5, 0, 12),(-8, -12, 0)]` is a skew symmetric matrix.
Explanation:
Let A = `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]`
A' = `[(0, 5, -8),(-5, 0, -12),(8, 12, 0)]`
⇒ A' = `-[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` = – A
A' = – A
So A is a skew-symmetric matrix.
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