Prove that the matrix is invertible for all values of the co

Prove that the matrix is invertible for all values of the constant k and find the inverse of A.

Solution

to become invertible , then det A should not be equal to zero

1 (2*2 - 2*3) -k (1*2 - 2*1 ) + 1 (1*3 -1*2) = det A

det A = (4 - 6) - k(2 -2) +3 (1)

det A = -2 + -k(0) +3

det A = 1 -k(0)

det A = 1

so

the det A is not equal to zero

the given matrix is invertiable for all values of \'k\' because always K*0 is always leads to zero

so hence proved

we can\'t find A inverse if we know \'k\' value then only we can find A inverse.