Question

Does the given matrix have a multiplicative inverse and explain your answer
a) matrix 2 5
b) matrix
4
8
c)matrix 0 0
0 0
d) matrix
1 0
0 1

Answer 1

Matrix A and B does not have a multiplicative inverse since they are not square matrix.Also C does not have a multiplicative inverse as its determinant is zero.Therefore only D has a multiplicative inverse as it is a square matrix and its determinant is not equal to zero

Answer 2

Remember: Only square matrices will have multiplicative inverse.

Therefore, matrix [2 5] and matrix $\left[\begin{array}{ccc}4\\8\end{array}\right]$ has no multiplicative inverse.

c) As the given matrix is a zero matrix, it has no inverse.

d) The given matrix is an identity matrix. Every identity matrix has its own inverse.