Without expanding proof that `|[1,2,3],[4,5,6],[7,8,9]|`=0

Using the property of determinants and without expanding, prove that: |[2, 7, 65],[ 3 ,8 ,75 ],[4, 9,86]|=0

Using the property of determinants and without expanding, prove that |(2,7,65), (3,8,75), (5,9,86)|=0

Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]|

Find the matrix X so that X[[1 ,2 ,3], [4, 5 ,6]]=[[-7,-8,-9],[2,4,6]]

Find the matrix X so that X[[1, 2, 3],[ 4 ,5, 6]] = [[-7,-8,-9],[2,4,6]]

Find the matrix X so that X[[1, 2, 3],[ 4 ,5, 6]] = [[-7,-8,-9],[2,4,6]]

No. of even 6 digits numbers, without repetition of digits, using digits 1,2,3,4,5,6,7 are:

Prove without expanding the determinant |(9, 9, 12),(1, -3, -4),(1, 9, 12)|=0 .

If a digit is chosen at random from the digits 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9 , then the probability that the digit is even, is (a) 4/9 (b) 5/9 (c) 1/9 (d) 2/3

If a digit is chosen at random from the digits 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9 , then the probability that it is odd, is (a) 4/9 (b) 5/9 (c) 1/9 (d) 2/3