Matrix Inverse, the Determinant, and Matrix Equations (VCE SSCE General Mathematics): Quizzes

$AA^{-1} = A^{-1}A = I$

A matrix with 1s on main diagonal, 0s elsewhere

$10$

Its determinant must be non-zero

A matrix with zero determinant, no inverse

$\frac{1}{ad-bc}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$

Show that $AB = I$ and $BA = I$

No, $AB \neq BA$ in general

Pre-multiply both sides by $B^{-1}$: $X = B^{-1}C$

Post-multiply both sides by $B^{-1}$: $X = CB^{-1}$