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Standard XII

Mathematics

Square Matrix

For a square ...

Question

For a square matrix $A$ and a non-singular matrix $B$ of the same order, value of determinant of $B^{- 1} A B$ is

| A |

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| B |

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∣ ∣ B^{- 1} ∣ ∣

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∣ ∣ A^{- 1} ∣ ∣

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Solution

The correct option is D $| A |$
$∣ ∣ B^{- 1} A B ∣ ∣ = ∣ ∣ B^{- 1} ∣ ∣ | A | | B |$
$= ∣ ∣ ∣ \frac{1}{B} ∣ ∣ ∣ | A | | B | = | A |$

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If A, B are square matrices of order 3, A is non-singular and AB = O, then B is a
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For a square matrix A and a non-singular matrix B of the same order, value of determinant of B−1AB is

The correct option is D |A|∣∣B−1AB∣∣=∣∣B−1∣∣|A||B| =∣∣∣1B∣∣∣|A||B|=|A|

For a square matrix $A$ and a non-singular matrix $B$ of the same order, value of determinant of $B^{- 1} A B$ is

The correct option is D $| A |$
$∣ ∣ B^{- 1} A B ∣ ∣ = ∣ ∣ B^{- 1} ∣ ∣ | A | | B |$
$= ∣ ∣ ∣ \frac{1}{B} ∣ ∣ ∣ | A | | B | = | A |$