Find the Inverse of a If It Has One, or State

question 105

Multiple Choice

Find the inverse of A if it has one, or state that the inverse does not exist.
- $$A = \left[ \begin{array} { r r r } 6 & 0 & 0 \\0 & - 6 & 0 \\6 & 0 & 6\end{array} \right]$$

• A)
• \[\left[ \begin{array} { c c c }
• \frac { 1 } { 6 } & 0 & 0 \\
• 0 & - \frac { 1 } { 6 } & 0 \\
• - \frac { 1 } { 6 } & 0 & \frac { 1 } { 6 }
• \end{array} \right]\]
• B) Inverse does not exist
• C)
• \[\left[ \begin{array} { r r r }
• - 6 & 0 & 0 \\
• 0 & 6 & 0 \\
• - 6 & 0 & - 6
• \end{array} \right]\]
• D)
• \[\left[ \begin{array} { c c c }
• - \frac { 1 } { 6 } & 0 & 0 \\
• 0 & \frac { 1 } { 6 } & 0 \\
• \frac { 1 } { 6 } & 0 & - \frac { 1 } { 6 }
• \end{array} \right]\]

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Definitions:

HAc

A shorthand notation for acetic acid, a colorless liquid organic compound with the chemical formula CH3COOH.

K

Symbol for Potassium, a soft, silvery-white metallic element essential for plant growth and human nutrition.

M

In the context of concentration, M stands for molarity, a measure of the concentration of a solute in a solution, defined as moles per liter.

Equilibrium Reaction

A chemical reaction in which the forward and reverse reactions occur at the same rate, so that the concentrations of the reactants and products do not change with time.