Matrices Cofactors

Find the determinant of the following matrix.

• -12

• -10

• 12

• 10

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Find the determinant of the following matrix.

• 8

• -8

• 18

• -18

Find the determinant of matrix B.

Find the determinant of the following matrix.

• -15

• 15

• 18

• -18

Which of the following is true

• If any two rows / columns are interchanged then value of the determinant remains unchanged.

• If any two rows/ columns are interchanged then value of the determinant becomes two times.

• If any two rows / columns are interchanged then value of the determinant changes by minus sign.

• If any two rows/ columns are interchanged then value of the determinant becomes zero.

Which of the following is not true

• If any two rows / columns of a determinant are identical then the value of determinant is zero.

• If each element of a row / column of a determinant is multiplied by the same number k , then value of the new determinant is k times the value of original determinant.

• If A and B are square matrices of same order then |AB| = |A|.|B|

• If A is a square matrix then |A| = the sum of the products elements of any row/column with the cofactors of the corresponding elements of some other row/column

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• 
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From the given determinant supply the needed minor of the element 5.

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Find the determinant of the following matrix.

• -7

• 7

• -23

• 23