Question:

Let $S=\{M=[a_{ij}],a_{ij}\in\{0,1,2\},1\leq i,j\leq2\}$ and $A=\{M\in S: M\text{ is invertible}\}$. Then $P(A)$ is equal to

\dfrac{16}{27}

\dfrac{47}{81}

\dfrac{49}{81}

\dfrac{50}{81}

Step-by-Step Solution

Key Concept: Total matrices: $3^4=81$. Invertible: $\det\neq0$. Count non-invertible (singular) matrices and subtract from 81.

$P(A)=\frac{50}{81}$.

Correct Answer: 4