Question

Write the properties of inverse of matrices​

Answer 1

(A-1)-1 =A

(AB)-1 =A-1B-1

(ABC)-1 =C-1B-1A-1

(A1 A2….An)-1 =An-1An-1-1……A2-1A1-1

(AT)-1 =(A-1)T

(kA)-1 = (1/k)A-1

AB = In, where A and B are inverse of each other.

If A is a square matrix where n>0, then (A-1)n =A-n

Where A-n = (An)-1

Answer 2

Answer:

Matrix Inverse Properties

The list of properties of matrices inverse is given below. Go through it and simplify the complex problems.

If A and B are the non-singular matrices, then the inverse matrix should have the following properties

(A-1)-1 =A

(AB)-1 =A-1B-1

(ABC)-1 =C-1B-1A-1

(A1 A2….An)-1 =An-1An-1-1……A2-1A1-1

(AT)-1 =(A-1)T

(kA)-1 = (1/k)A-1

AB = In, where A and B are inverse of each other.

If A is a square matrix where n>0, then (A-1)n =A-n

Where A-n = (An)-1

Step-by-step explanation:

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