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  • State True or False for the statements (aA)-1 = (1/a) A-1, where a is any real number and A is a square matrix.

State True or False for the statements

(aA)^{-1} = (1/a) A^{-1}, where a is any real number and A is a square matrix.

Answers (1)

For a non singular matrix, aA is invertible such that

\\ (\mathrm{aA})\left(\frac{1}{\mathrm{a}} \mathrm{A}^{-1}\right)=\left(\mathrm{a} \cdot \frac{1}{\mathrm{a}}\right)\left(\mathrm{AA}^{-1}\right) \\ \text {i.e. } \quad(\mathrm{aA})^{-1}=\frac{1}{\mathrm{a}} \mathrm{A}^{-1} \\

here a = any non-zero scalar. Here A should be a non-singular matrix which is not given in the statement, thus the statement given in question in false.

 

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infoexpert22

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