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Q.

If A is any square matrix. Observe the following lists and matching from List-I to List- II is
List-I List-II
A) A² = A 1) Orthogonal matrix
B) A² = I 2) Symmetric matrix
C) A² = 0 3) Idempotent matrix
D) A.A^T = A^T.A = I 4) Nilpotent matrix
5) Involutory matrix

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a

$A \to 2, B \to 5, C \to 4, D \to 1$

b

$A \to 3, B \to 2, C \to 4, D \to 1$

c

$A \to 3, B \to 5, C \to 4, D \to 1$

d

$A \to 3, B \to 5, C \to 4, D \to 2$

answer is C.

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Detailed Solution

A matrix is said to be Orthogonal matrix if A.A^T = A^T.A = I.

A matrix is said to be Involutory matrix if and only if A² = I, where I is the n × n identity matrix.

A matrix is said to be idempotent matrix if A² = A.

A square matrix A is said to be a nilpotent matrix of degree n if Aⁿ=0

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