Question

For which values of a does ???? a a − 4 a + 4 a ???? have an inverse matrix?

Answer 1

Answer:

A =  $\dfrac{1}{16}\begin{bmatrix}a &-(a-4) \\ -(a+4) & a\end{bmatrix}$

Step-by-step explanation:

given,

Matrix =

A = $\begin{bmatrix}a &a-4 \\ a+4 & a\end{bmatrix}$

determinant of matrix

|A| = a×a - (a-4)(a+4)

|A| = a² - a² +16

|A| = 16

inverse of the matrix

to calculate inverse of two matrix interchange the term a₁₁ with a₂₂ and multiply the -ve with a₁₂ and a₂₁

the inverse is

A =  $\dfrac{1}{16}\begin{bmatrix}a &-(a-4) \\ -(a+4) & a\end{bmatrix}$