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PUNE MCA Exam 2014 Question Paper with answers for online practice

Question : 40 of 58

Marks: +1, -0

If AA

^T

I

& det A = 1 then which is correct

Solution:

Concept:

AA^T = I

means

A

is orthogonal, and

\det A = 1

means

A

is a rotation matrix.

Explanation:

An orthogonal matrix with determinant 1 can be any rotation matrix, e.g., in 2D:

A = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}

This matrix satisfies

AA^T = I

and

\det A = 1

, but

A \neq I

A \neq -I

, and

A \neq 2I

Therefore, none of the given options is always true.

Answer:

None of these

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