The determinant of the transpose of a square matrix is equal to the determinant of the matrix, that is,
det(AT)=det(A) 2.1
A=[−432−3]
−A=[4−3−23]
det(−A)=∣∣4−3−23∣∣=4(3)−(−2)(−3)=18
AT=[−432−3]T=[−423−3]
−AT=[4−2−33]
det(−AT)=∣∣4−2−33∣∣=4(3)−(−2)(−3)=18
det(−A)=det(−AT)
2.2
A=⎣⎡3−5−1130−2−6−4⎦⎤
−A=⎣⎡−351−1−30264⎦⎤
det(−A)=∣∣−351−1−30264∣∣
=1∣∣−1−326∣∣−0∣∣−3526∣∣+4∣∣−35−1−3∣∣
=−6+6+4(9+5)=56
AT=⎣⎡3−5−1130−2−6−4⎦⎤T=⎣⎡31−2−53−6−10−4⎦⎤
−AT=⎣⎡−3−125−36104⎦⎤
det(−AT)=∣∣−3−125−36104∣∣
=1∣∣−12−36∣∣−0∣∣−3256∣∣+4∣∣−3−15−3∣∣
=−6+6−9+4(9+5)=56
det(−A)=det(−AT)
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