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If A is a square matrix of order 3 and A=4|A| = 4, then the value of 2AT|2A^T| is

Solution

Correct Option: 4

Given that AA is a square matrix of order 3 and A=4|A| = 4.

The order 3 means AA is a 3×33 \times 3 matrix.


For the transpose property:

AT=A|A^T| = |A|

Therefore:

AT=4|A^T| = 4


When a matrix is multiplied by a scalar kk, the determinant follows:

kA=kn×A|kA| = k^n \times |A|

where nn is the order of the matrix.


For 2AT|2A^T| where k=2k = 2 and n=3n = 3:

2AT=23×AT|2A^T| = 2^3 \times |A^T|

2AT=8×4|2A^T| = 8 \times 4

2AT=32|2A^T| = 32

Therefore, the value of 2AT=32|2A^T| = 32.

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