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Does the given matrix have a multiplicative inverse and explain your answer

a) matrix 2 5
b) matrix
c)matrix 0 0
0 0
d) matrix
1 0
0 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
2 5 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.
1 5 1
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