87a763…: “To the loud cat”

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True/False. Every matrix has an inverse.

True False

If $A$ and $B$ are invertible, then:

$(AB)^{-1} = A^{-1}B^{-1}$ $(AB)^{-1} = B^{-1}A^{-1}$

Compute the determinant of $A=\begin {bmatrix} 2& 1\\ 3&5 \end {bmatrix}$ .

$\det A = \answer {7}$

Is $A$ invertible?

Yes No

Compute the determinant of $A=\begin {bmatrix} 2& 1\\ 6&3 \end {bmatrix}$ .

$\det A = \answer {0}$

Is $A$ invertible?

Yes No

Compute the determinant of $A=\begin {bmatrix} 0& -1\\ -4&5 \end {bmatrix}$ .

$\det A = \answer {-4}$

What is $A^{-1}$ ?

$A^{-1} = \dfrac {1}{\answer {-4}} \left [ \begin {array}{cc} \answer {5} &\answer {1} \\ \answer {4} &\answer {0} \end {array}\right ]$