Question

The inverse of a matrix doesn't exists if the matrix is​

Answer 1

Answer:

Not all 2 × 2 matrices have an inverse matrix. If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses.

Answer 2

SOLUTION

TO DETERMINE

The inverse of a matrix doesn't exists if the matrix is __

EVALUATION

Let A be a matrix

By the definition of inverse of a matrix

$\sf {A}^{ - 1} = \dfrac{adj \:A }{ |A| }$

So inverse of the matrix A doesn't exists if

| A | = 0

Again we know that a matrix A is said to be singular if | A | = 0

Hence the inverse of a matrix doesn't exists if the matrix is singular

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