If is a matrix satisfying AA' = 9I, find x.

Given:

•

So, finding AA’ we get which is also equal to 9I.

Now, =

Equating same terms, we get 2x + 4 = 0

x = –2

Putting x = –2 in AA’ we get

∴x = –2

Hence, the value of x is equal to –2.

Note: We can find the value of x only by calculating the a₁₂ element, So, there is no need to multiply the full matrix.