Matrix Quiz

For what positive, real value of A is the determinant of the matrix \(
\begin{bmatrix}
A & 2 \\
1 & 2
\end{bmatrix}\) equal to A?

**(Note: The determinant of any matrix \(
\begin{bmatrix}
A & B \\
C & D
\end{bmatrix}\) equals ad − bc.)

For what positive, real value of X is the determinant of the matrix \(
\begin{bmatrix}
X & 2 \\
X & X
\end{bmatrix}\) equal to X?

**(Note: The determinant of any matrix \(
\begin{bmatrix}
A & B \\
C & D
\end{bmatrix}\) equals ad − bc.)

What positive, real value of Q satisfies
the given equation \(Q*\begin{bmatrix}
2 & 2 \\
1 & 0
\end{bmatrix}=
\begin{bmatrix}
4 & 4 \\
2 & 0
\end{bmatrix}\) equal to X?

**(Note: The determinant of any matrix \(
\begin{bmatrix}
A & B \\
C & D
\end{bmatrix}\) equals ad − bc.)

What positive, real value of Q satisfies
the given equation \(Q*\begin{bmatrix}
2 & 2 \\
1 & 0
\end{bmatrix}=
\begin{bmatrix}
4 & 4 \\
2 & 0
\end{bmatrix}\) equal to X?

**(Note: The determinant of any matrix \(
\begin{bmatrix}
A & B \\
C & D
\end{bmatrix}\) equals ad − bc.)