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Question

If A=[λμμ2λ2λμ]A=[λμμ2−λ2−λμ] then A2 is

A
an idempotent matrix
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B
a nilpotent matrix
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C
an orthogonal matrix
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D
a symmetric matrix
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Solution

The correct option is B a nilpotent matrix
Given A=[λμμ2λ2λμ]

A2=[λμμ2λ2λμ][λμμ2λ2λμ]

=[0000]

Hence, A2=0

The matrix A is said to be Nilpotent if Am=0 where m is an integer and 0 is a null matrix of the same order as of A.

Hence, A2 is a nilpotent matrix.

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