Question

For where it says "choose" is either is/is not or are/are not

Answer 1

Answer: Is and Are

Explanation:

i took the test and those were correct :)

Answer 2

IS NOT; ARE NOT

Explanation:

Given:
`\[  \begin{bmatrix}    (1)/(4) & (1)/(4)\\    \\-1 & (-1)/(2) \end{bmatrix}\]`

and
`\[A =  \begin{bmatrix}    (1)/(4) & (1)/(4) \\\\    -1 & (-1)/(2)  \end{bmatrix}\]`

We say two matrices
`$ A $` and
`$ B $` are inverses of each other when
`$ AB = BA = I $` where
`$ I $` is the identity matrix.

`\[I =  \begin{bmatrix}    1 & 0\\    0 & 1  \end{bmatrix}\]`

So, for
`$ X $` and
`$ A $` to be inverses of each other, we should have
`$ AX = XA = I $`.

Let us calculate
`$ XA $`.

`\[\begin{bmatrix} -2 & -1 \\ 8 & 2 \end{bmatrix}\]`
`\[\begin{bmatrix} (1)/(4) & (1)/(4) \\\\ -1 & (-1)/(2)\end{bmatrix}\]`
`$ = $`
`\[\begin{bmatrix}(1)/(2) & 0 \\0 & 0 \end{bmatrix}\]`

This is clearly not equal to the identity matrix. So we conclude that the matrices are not inverses of each other.