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10 questions from this quiz
AA−1=A−1A=IAA^{-1} = A^{-1}A = IAA−1=A−1A=I
A matrix with 1s on main diagonal, 0s elsewhere
101010
Its determinant must be non-zero
A matrix with zero determinant, no inverse
1ad−bc[d−b−ca]\frac{1}{ad-bc}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}ad−bc1[d−c−ba]
Show that AB=IAB = IAB=I and BA=IBA = IBA=I
No, AB≠BAAB \neq BAAB=BA in general
Pre-multiply both sides by B−1B^{-1}B−1: X=B−1CX = B^{-1}CX=B−1C
Post-multiply both sides by B−1B^{-1}B−1: X=CB−1X = CB^{-1}X=CB−1
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