If determinant of matrix - a b c- d e f- g h i - is A- then determinant of - a d g- b e h- c f i - isA- AB- - AC- A2D- -A2

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Byju's Answer

Standard XII

Mathematics

Scalar Matrix

If determinan...

Question

If determinant of matrix $∣ ∣ ∣ ∣ \begin{matrix} a & b & c d & e & f g & h & i \end{matrix} ∣ ∣ ∣ ∣$ is A , then determinant of $∣ ∣ ∣ ∣ \begin{matrix} a & d & g b & e & h c & f & i \end{matrix} ∣ ∣ ∣ ∣$ is

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-A

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A^{2}

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A^{2}

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Solution

The correct option is A A
If we clearly see that second matrix is the transpose of the first one. And we already know that determinant of the transpose of a matrix is same as the original one. So if determinant of the original one is A then the determinant of the second one will be A as well

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If determinant of matrix ∣∣ ∣∣abcdefghi∣∣ ∣∣ is A , then determinant of ∣∣ ∣∣adgbehcfi∣∣ ∣∣ is

The correct option is A AIf we clearly see that second matrix is the transpose of the first one. And we already know that determinant of the transpose of a matrix is same as the original one. So if determinant of the original one is A then the determinant of the second one will be A as well

If determinant of matrix $∣ ∣ ∣ ∣ \begin{matrix} a & b & c d & e & f g & h & i \end{matrix} ∣ ∣ ∣ ∣$ is A , then determinant of $∣ ∣ ∣ ∣ \begin{matrix} a & d & g b & e & h c & f & i \end{matrix} ∣ ∣ ∣ ∣$ is

The correct option is A A
If we clearly see that second matrix is the transpose of the first one. And we already know that determinant of the transpose of a matrix is same as the original one. So if determinant of the original one is A then the determinant of the second one will be A as well