If $A$ and $B$ are non singular matrix of same order such that $| A B | = 10, | A | = 5.$ Then the value of $(| A | - | B |)^{2}$ is:

9

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49

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41

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4

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Solution

The correct option is A $9$
$(| A | - | B |)^{2} = | A |^{2} + | B |^{2} - 2 | A | | B | | A B | = | A | | B | = 10 \Rightarrow | B | = 2 (| A | - | B |)^{2} = 25 + 4 - 20 = 9$

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If A and B are non singular matrix of same order such that |AB|=10, |A|=5. Then the value of (|A|−|B|)2 is:

The correct option is A 9(|A|−|B|)2=|A|2+|B|2−2|A||B||AB|=|A||B|=10⇒|B|=2(|A|−|B|)2=25+4−20=9

If $A$ and $B$ are non singular matrix of same order such that $| A B | = 10, | A | = 5.$ Then the value of $(| A | - | B |)^{2}$ is:

The correct option is A $9$
$(| A | - | B |)^{2} = | A |^{2} + | B |^{2} - 2 | A | | B | | A B | = | A | | B | = 10 \Rightarrow | B | = 2 (| A | - | B |)^{2} = 25 + 4 - 20 = 9$