Q. 15

# Using properties of determinants, prove the following:

Answer :

R_{1}→R_{1} + bR_{3}

taking common (1 + a^{2}+ b^{2})

R_{2}→R_{2} – aR_{3}

Taking common (1 + a^{2}+ b^{2})

= (1+a^{2}+b^{2} )^{2} (1- a^{2}-b^{2} +2a^{2}+2a^{2})

= (1+a^{2}+b^{2} )^{2} (1+a^{2}+b^{2} )

= (1+a^{2}+b^{2} )^{3}

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