Thread: [SOLVED] Finding a determinant (matrix)

1. [SOLVED] Finding a determinant (matrix)

I just don't know how to start, so I'd like a push.
Let $\displaystyle A$ and $\displaystyle B$ be $\displaystyle 2\times 2$ matrices that satisfies $\displaystyle A^2B=3I$ and $\displaystyle A^TB^3=-I$, where $\displaystyle I$ is the identity matrix. Calculate $\displaystyle \det(A)$.

2. Hello !
Originally Posted by arbolis
I just don't know how to start, so I'd like a push.
Let $\displaystyle A$ and $\displaystyle B$ be $\displaystyle 2\times 2$ matrices that satisfies $\displaystyle A^2B=3I$ and $\displaystyle A^TB^3=-I$, where $\displaystyle I$ is the identity matrix. Calculate $\displaystyle \det(A)$.
$\displaystyle \text{det}(A^T)=\text{det}(A)$ and $\displaystyle \text{det}(AB)=\text{det}(A) \times \text{det}(B)$

3. and
ah.... the basic properties of the determinant.
I reached $\displaystyle \det(A)=-4$ and $\displaystyle \det(B)=-1$. If you have time to check out the answer, I'd be glad. Otherwise it doesn't matter that much.