The matrix is not square, so it does not have an inverse.

To determine the inverse of a matrix, you must first verify that the matrix is square.  Next calculate the determinant.  The determinant for this matrix is 0, so it does not have an inverse. 

The matrix is square, so it could have an inverse.  Next you need to find the determinant which is -6.  Swap the numbers in spots a and d and put a negative in front of the numbers in spots b and c. 

 then divide each number by the determinant and simplify. 

The matrix is square, so it could have an inverse.  Next, calculate the determinant.  The determinant for this matrix is 0 so it does not have an inverse. 

A matrix must be square to have an inverse.  This matrix is square, so it could have an inverse.  Next the determinant of the matrix must not be 0 to have an inverse.  The determinant of this matrix is -6, so it has an inverse.  To find the inverse of a 3x3 matrix, first write it in augmented form. 

Next find the pivot in the first column by dividing R1/2.

Next, eliminate the first column by subtracting R2-5R1 and R3-2R1

Next, find the pivot in column 2 by dividing -7R2/2

Next, eliminate the second column by subtracting R1-3R2/2 and R3+2R2

Next find the pivot in column 3 by dividing 6R3/7

Finally, Eliminate the third column by subtracting R1-20R3/7 and R2-

Now that we have the identity matrix on the left side, the right side is our answer.

The matrix must be square to have an inverse. This matrix is square so it could have an inverse.  A matrix must also have a non-zero determinant.  The determinant for this matrix is zero, so it does not have an inverse. 

To find the inverse of a matrix first look to verify that the matrix is square.  If it is not square, it does not have an inverse. Next, you must find the determinant.  If the determinant is 0, then the matrix does not have an inverse.  The determinant for this matrix is ad-bc = 16, therefore it has an inverse.  To find the inverse of a 2x2 matrix we first write it in augmented form.

    First we will swap rows 1 and 2  next we will eliminate the first column by taking R2-2R1 , next we will divide R2/16 to set the second pivot. . Next we will eliminate the second column by taking R1-4R2. . Now that we have the identity matrix on the left, our answer is on the right.  There is, however, an easier way to determine the inverse of a 2x2 matrix.  The trick is to swap the numbers in spots a and d, put negatives in front of the numbers in spots b and c and then divide everything by the determinant.  For this example,  then divide by the determinant which is 16 and simplify. 

To determine the inverse of a matrix, you must first verify that the matrix is square.  Next calculate the determinant.  The determinant for this matrix is -2.  Now you can swap the numbers in a and d and put a negative in front of the numbers in b and c.   once you have done that, then you divide each number by the determinant.  

The matrix is square, so it could have an inverse.  Next you need to find the determinant which is 362.  Swap the numbers in spots a and d and put a negative in front of the numbers in spots b and c. 

 then divide each number by the determinant and simplify. 

Only a square matrix - a matrix with an equal number of rows and columns - has an inverse. Therefore, a matrix with five rows and four columns cannot even have an inverse.