Question

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

Answer 1

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

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 =
`(1)/(16)\begin{bmatrix}a &-(a-4) \\ -(a+4) & a\end{bmatrix}`