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  • State True or False for the statements If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

State True or False for the statements

If A and B are matrices of order 3 and |A| = 5, |B| = 3, then |3AB| = 27 × 5 × 3 = 405.

 

Answers (1)

We know that:
\\ \vspace{\baselineskip} \vert AB \vert = \vert A \vert \cdot \vert B \vert \\ and if A = [a_{ij}]_{3 \times 3}, then \vert k.A \vert = k^{3} \vert A \vert.

\\ \vspace{\baselineskip} \therefore \vert 3A \vert = 27 \vert AB \vert \\ \\ \vspace{\baselineskip} = 27 \vert A \vert \vert B \vert \\ \\ \vspace{\baselineskip} = 27 \cdot 5 \cdot 3\\ \\ \vspace{\baselineskip} = 405\\ \vspace{\baselineskip}

Hence the statement given in question is true.

Posted by

infoexpert22

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