If A=[aij]3x3 is any orthogonal matrix then which of the following can

1.	If A=[aij]3x3 is any orthogonal matrix then which of the following cannot be true. \|A\| = 1\|A\| = -1\|A\|=0None of these
Answer» \(\because\) A is orthogonal matrix. \(\therefore \) A^TA = A.A^T = I, where I is identify matrix. ⇒ \|A^TA\| = \| I \| ⇒ \|A^TA\| \|A\| = 1 (\(\because\) \| I \| = 1) ⇒ \|A\| \|A\| = 1 (\(\because\) \|A^TA\| = \|A\|) ⇒ \|A\|² = 1 ⇒ \|A\| = -1 or \|A\| = 1 Hence, \|A\| = 0 can not be true for an orthogonal matrix A.

If A=[aij]3x3 is any orthogonal matrix then which of the following cannot be true. |A| = 1|A| = -1|A|=0None of these

Answer»

\(\because\) A is orthogonal matrix.

\(\therefore \) A^TA = A.A^T = I, where I is identify matrix.

⇒ |A^TA| = | I |

⇒ |A^TA| |A| = 1 (\(\because\) | I | = 1)

⇒ |A| |A| = 1 (\(\because\) |A^TA| = |A|)

⇒ |A|² = 1

⇒ |A| = -1 or |A| = 1

Hence, |A| = 0 can not be true for an orthogonal matrix A.

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If A=[aij]3x3 is any orthogonal matrix then which of the following cannot be true. |A| = 1|A| = -1|A|=0None of these

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