If A is an invertible matrix and A^{-1} = ((3,4),(5,6)) then A = ? ​

Question

If A is an invertible matrix and A^-1 = \(\begin{pmatrix} 3&4 \\ 5 &6 \end{pmatrix}\)then A = ?

A.\(\begin{pmatrix} 6&-4 \\ -5 &3 \end{pmatrix}\)

B.\(\begin{pmatrix} 1/3&1/4 \\ 1/5 &1/6 \end{pmatrix}\)

C.\(\begin{pmatrix} -3&2\\ 5/2 &-3/2 \end{pmatrix}\)

D. None of these

Answer 1

y property of inverse 

(A -1)^-1 = A

(A^-1)^-1 = \(\begin{pmatrix} 3&4 \\ 5 &6 \end{pmatrix}^{-1}\)

A = \(\begin{pmatrix} 3&4 \\ 5 &6 \end{pmatrix}^{-1}\)........1

|A|^-1 = 3 x 6 – 4 x 5 

- 2 

C₁₁ = 6 C₁₂ = - 5 

C₂₁= -4 C₂₂ = 3 

Cofactor matrix A = \(\begin{pmatrix} 6&-5 \\ -4 &3 \end{pmatrix}\)

Putting in 1

A = \(\begin{pmatrix} -3&2\\ 5/2 &-3/2 \end{pmatrix}\)