Let the determinant of a 3- 3 matrix A be 6- then B is a matrix defined by B-5A2- Then determinant of B is-

The correct option is A 180 3× 3 Matrix | A | =6 B=5 A ^ 2 We know | A | #160; ^ 2 =| A ^ 2 | | B | =5| A | #160; ^ 2 ⇒ ...

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Standard XII

Mathematics

Definition of a Determinant

Let the deter...

Question

Let the determinant of a $3 \times 3$ matrix A be $6$ , then B is a matrix defined by $B = 5 A^{2}$ . Then determinant of B is.

180

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80

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None of these

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Solution

The correct option is A $180$
$3 \times 3$ -Matrix
$| A | = 6$
$B = 5 A^{2}$
We know ${| A |}^{2} = ∣ ∣ A^{2} ∣ ∣$
$| B | = 5 {| A |}^{2}$
$\Rightarrow | B | = 5 {(6)}^{2} = 5 \times 36$
$= 180$

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Let the determinant of a 3×3 matrix A be 6, then B is a matrix defined by B=5A2. Then determinant of B is.

The correct option is A 1803×3-Matrix|A|=6B=5A2We know |A|2=∣∣A2∣∣|B|=5|A|2⇒|B|=5(6)2=5×36=180

Let the determinant of a $3 \times 3$ matrix A be $6$ , then B is a matrix defined by $B = 5 A^{2}$ . Then determinant of B is.

The correct option is A $180$
$3 \times 3$ -Matrix
$| A | = 6$
$B = 5 A^{2}$
We know ${| A |}^{2} = ∣ ∣ A^{2} ∣ ∣$
$| B | = 5 {| A |}^{2}$
$\Rightarrow | B | = 5 {(6)}^{2} = 5 \times 36$
$= 180$