What is the real value of that makes the matrix have a multiplicative inverse?
A matrix has a multiplicative inverse if and only if its determinant is not equal to 0. First find an expression for the determinant of matrix :
This expression then factorises as
To find the values of for which the matrix will not have a multiplicative inverse, set this equal to 0:
Therefore, the matrix has a multiplicative inverse for all real values of apart from 11 and . This can be written as .