# [SOLVED]Show Matrix A is not invertible

#### delgeezee

##### New member
SHow that matrix A is not invertible, where
A =
 $$\displaystyle cos^2 \alpha$$ $$\displaystyle sin^2 \beta$$ $$\displaystyle cos^2 \theta$$ a a a $$\displaystyle sin^2 \alpha$$ $$\displaystyle cos^2 \beta$$ $$\displaystyle sin^2 \theta$$

#### tkhunny

##### Well-known member
MHB Math Helper
Have you considered the Determinant?

#### delgeezee

##### New member
Have you considered the Determinant?
Yes i know if the det = 0 then the matrix is not invertible, or if i can introduce a row or columns of zeros its not invertible.

im not sure but maybe there is something involved with transformations.

#### Petrus

##### Well-known member
Yes i know if the det = 0 then the matrix is not invertible, or if i can introduce a row or columns of zeros its not invertible.

im not sure but maybe there is something involved with transformations.
Hello delgeezee,
If matrice $$\displaystyle A$$ is invertible Then $$\displaystyle A^T$$ is Also invertible
Regards,
$$\displaystyle |\pi\rangle$$

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Welcome to MHB, delgeezee! Yes i know if the det = 0 then the matrix is not invertible, or if i can introduce a row or columns of zeros its not invertible.

im not sure but maybe there is something involved with transformations.
Yes. It involves transformations that are applicable to determinants.
In particular you can add or subtract a multiple of any row to another row.
The determinant will remain the same under such a transformation.

#### Petrus

##### Well-known member
Welcome to MHB, delgeezee! Yes. It involves transformations that are applicable to determinants.
In particular you can add or subtract a multiple of any row to another row.
The determinant will remain the same under such a transformation.
Hello,
After I read I like Serena post I realised I missunderstand you did not ask about transport..
I will citate from Ackbach:
"The ERO that takes a multiple of one row, adds it to another row, and stores it in that row, does not change the determinant.

The ERO that switches two rows multiplies the determinant by $-1$.

The ERO that multiplies a row by a nonzero number $m$ also multiplies the determinant by $m$"

Regards,
$$\displaystyle |\pi\rangle$$

#### delgeezee

##### New member
Hello,
After I read I like Serena post I realised I missunderstand you did not ask about transport..
I will citate from Ackbach:
"The ERO that takes a multiple of one row, adds it to another row, and stores it in that row, does not change the determinant.

The ERO that switches two rows multiplies the determinant by $-1$.

The ERO that multiplies a row by a nonzero number $m$ also multiplies the determinant by $m$"

Regards,
$$\displaystyle |\pi\rangle$$
Thank I was able to introduce a row of zeros by reducing the determinant matrices to upper triangular form thus making the determinant = 0 by taking the cofactor expansion along the row of zeros.