matrices

The statements P and Q are related to matrices A and B, which are conformable for both addition and multiplication. P: (A + B)ᵀ = Aᵀ + Bᵀ Q: (AB)ᵀ = AᵀBᵀ Which one of the following...

The statements P and Q are related to matrices A and B , which are conformable for both addition and multiplication. P: $(A + B)^T = A^T + B^T$ Q: $(AB)^T = B^T A^T$ Which one of t...

P and Q are two square matrices of the same order. Which of the following statement(s) is/are correct?

The matrix $$P$$ is the inverse of a matrix $$Q.$$ If $${\rm I}$$ denotes the identity matrix, which one of the following options is correct?

If $$A = \left[ {\matrix{ 1 & 5 \cr 6 & 2 \cr } } \right]\,\,and\,\,B = \left[ {\matrix{ 3 & 7 \cr 8 & 4 \cr } } \right]A{B^T}$$ is equal to

Consider the following simultaneous equations (with $${c_1}$$ and $${c_2}$$ being constants): $$$3{x_1} + 2{x_2} = {c_1}$$$ $$$4{x_1} + {x_2} = {c_2}$$$ The characteristic equation...

Given the matrices $$J = \left[ {\matrix{ 3 & 2 & 1 \cr 2 & 4 & 2 \cr 1 & 2 & 6 \cr } } \right]$$ and $$K = \left[ {\matrix{ 1 \cr 2 \cr { - 1} \cr } } \right],\,\,$$ the product $...

The product of matrices $${\left( {PQ} \right)^{ - 1}}P$$ is

The determinant of the following matrix $$\left[ {\matrix{ 5 & 3 & 2 \cr 1 & 2 & 6 \cr 3 & 5 & {10} \cr } } \right]$$

If $$A,B,C$$ are square matrices of the same order then $${\left( {ABC} \right)^{ - 1}}$$ is equal be

If $$A$$ is a real square matrix then $$A{A^T}$$ is

If $$A$$ and $$B$$ are two matrices and $$AB$$ exists then $$BA$$ exists,