Find the Inverse of a 3 by 3 Matrix

A step by step worksheet to calculate the inverse of a 3 by 3 matrix is presented and as many practice questions as needed may be generated along with their solutions."> Solve each step below then click on "Show me" to check your answer.


Step by step solution


STEP 1: - Calcuate the determinant D of the given matrix. If D = 0, matrix A has non inverse.





STEP 2: - Determine the minors of the given matrix A and write down the matrix M of minors (How? for each element in the given matrix, ignore the row and column containing that elelemnt and calculate the determinant of the remaining smalller matrix).





STEP 3: - Determine C, the matrix of cofactors (Using the chart of signs shown below and matrix M to change the sign of any element in M if it corresponds to a minus sign in the chart.)

$\begin{vmatrix} + &- & + \cr - & + & - \cr+&-&+\end{vmatrix}$.





STEP 4: Determine $Ad$, the adjugate matrix of A (How? form a new matrix by changing the rows and columns of the matrix of cofactors C obtained in the last step).





STEP 4: Determine the inverse matrix $A^{-1}$ of $A$ using the formula: $A^{-1} = \dfrac{1}{D} Ad $.