Question

Which of the following matrix/matrices is/are invertible?

• A. A matrix of order 2 x 3
• B. An identity matrix
• C. A scalar matrix with diagonal elements not equal to 0.
• D. A diagonal matrix with diagonal elements as {2, 3, 5, 0, 1}

Answer 1

Answer: (B), (C)

The correct options are
B

An identity matrix

C

A scalar matrix with diagonal elements not equal to 0.

As we can see only a square matrix can have an inverse. It means a matrix of order $2\times 3$ cannot have an inverse.

We know that determinant of a diagonal or triangular matrix is the product of all diagonal elements of that matrix. In the matrix given in option (d) one of the diagonal element is given is 0 making the whole determinant to be zero. So matrix in option (d) is not invertible.

The identity and scalar matrix will be having 1 and a non-zero values respectively as a determinants. So in these cases matrices will be invertible.