Find the value of x for which the matrix product

Solution:

We know,

is identity matrix of size \[3\]

So according to the given criteria

Now we will multiply the two matrices on LHS using the formula \[{{c}_{ij}}~=\text{ }{{a}_{i1}}{{b}_{1j}}~+\text{ }{{a}_{i2}}{{b}_{2j}}~+\text{ }\ldots \text{ }+\text{ }{{a}_{in~}}{{b}_{nj}},\] we get

And to satisfy the above condition of equality, the corresponding entries of the matrices should be equal

So we get

So the value of \[x\] is