Determine the determinant of the matrix [12023−40401601020]. State whether the matrix has an inverse, but don't calculate the inverse.
Let
A=[12023−40401601020]
det(A)=[12023−40401601020]=0|202−404020|−1|102304120|+6|1223−44100|+0|1203−40102|
det(A)=−1|102304120|+6|1223−44100|
det(A)=−1[1(0⋅0−4⋅2)−0(3⋅0−4⋅1)+2(3⋅2−1⋅0)]+6[1(−4⋅0−4⋅0)−2(3⋅0−4⋅1)+2(3⋅0−(−4)⋅1)]
det(A)=−4+96
det(A)=92
The given matrix has an inverse.
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