(D) Given matrices: $P_{2 \times 3}$, $X_{4 \times 3}$, $Y_{4 \times 3}$.$X^T$ has order $3 \times 4$.$P^T$ has order $3 \times 2$.$X^T Y$ has order $

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(D) Given matrices: $P_{2 \times 3}$, $X_{4 \times 3}$, $Y_{4 \times 3}$.$X^T$ has order $3 \times 4$.$P^T$ has order $3 \times 2$.$X^T Y$ has order $(3 \times 4) \times (4 \times 3) = 3 \times 3$.$(X^T Y)^{-1}$ has order $3 \times 3$.$P(X^T Y)^{-1}$ has order $(2 \times 3) \times (3 \times 3) = 2 \times 3$.$P(X^T Y)^{-1} P^T$ has order $(2 \times 3) \times (3 \times 2) = 2 \times 2$.Finally, the transpose of a $2 \times 2$ matrix remains $2 \times 2$.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Types of matrices, Algebra of matrices

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If $X_{4 \times 3}$, $Y_{4 \times 3}$ and $P_{2 \times 3}$ are matrices, then the order of the matrix $\left[P(X^T Y)^{-1} P^T\right]^T$ is

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A
$4 \times 3$
B
$3 \times 4$
C
$3 \times 3$
D
$2 \times 2$

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3 and 4 .Determinants and Matrices

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Types of matrices, Algebra of matrices

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If $X_{4 \times 3}$, $Y_{4 \times 3}$ and $P_{2 \times 3}$ are matrices, then the order of the matrix $\left[P(X^T Y)^{-1} P^T\right]^T$ is

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