Back to Use matrix inverses to solve systems — Problem 1 · Task Set 47

HSA.REI.C.9 Tutor Intake — Matrix Inverses

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Grade 9·8 problems·~13 min·Common Core Math - HS Algebra·standard·hsa-rei-c-9

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Which of the following is the defining property of a matrix inverse $A^{-1}$ ?

$A^{-1}$ is the matrix obtained by swapping the rows and columns of $A$ .

$A^{-1}$ satisfies $AA^{-1} = A^{-1}A = I$ , where $I$ is the identity matrix.

$A^{-1}$ is obtained by dividing each entry of $A$ by the determinant.

$A^{-1}$ exists for every square matrix $A$ .