Question

If A' = -A where A is 3×3 matrix then |A| is equal to

pls ans if you know​

Answer 1

Answer:

We have been given the matrix equation here,

A' = -A

there will be some pre requisites required here to know

1) The determinant of the transpose of a matrix is equal to the determinant of the matrix itself.

or,

|A'| = |A|

This can be easily proved by expansion of any generic matrix and finding its determinant.

2) Also,

|kA| = k^order of matrix * |A|

where k is any scalar

So, now

We have been given the equation

A' = -A = (-1)*A

taking determinant on both sides,

|A'| = |(-1)A|

=>

|A| = (-1)^3 |A|

or,

|A| = -|A|

=>

2|A| = 0

or,

|A| = 0

Therefore, the determinant of the matrix A according to the given matrix equation will be zero.

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Answer 2

Answer:

hope it helped u !!

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