HELP ME PLEASE!!! MATRIX OPERATION: Perform the indicated operation using the given matrices.

Question

 

Find the inverse of A given that |A| = 5.

( I don't understand this)

Answer 1

Hello Lucy!

Must remember that the inverse of A is a matrix that if multiplied by A, the result is the identity matrix, in other words:

(a b) (1 -1) = (1 0)

(c d) (2 3) (0 1)

This will generate a 4 letters, 4 equations system:

a + 2b = 1

-a + 3b = 0

5b = 1

b = 1/5

a = 3/5

c + 2d = 0

-c + 3d = 1

5d = 1

d = 1/5

c = -2/5

Answer 2

The inverse matrix A^-1 has the property that

A.A^-1 = I (Identity matrix)

For a 2x2 matrix, A

A = |a b|

|c d|

Determinant |A| = ad-bc

For the given matrix A, you can easily use the formula

A^-1 = 1/(ad-bc) *|d -b|

|-c a|

Answer should be

A^-1 = 1/5 *|3 1|

|-2 1|

You can verify if AA^-1 = I, where the identity matrix is given by

I = |1 0|

|0 1|

Hope this makes it clear.